I actually like the fact that it looks very random from the outside, but when you stand on the center block it becomes a perfect circle. I really like chaotic designs like this and having them come together so beautifully is wonderful. I must build this in my hardcore world!
ill post the schematic of both the world and the armor stand tols in the schem channel in my discord, if you want to take it, or possibly make your own (if you have a bigger gradient)
@@kr1v you could switch between more colors. He didn't include the values or brown. You could also reuse colors in your gradient, or do something crazy with mixing 3 colors at once
@@squibble111 I was thinking of making a muuuuch bigger circle for one of the farms im cooking and I was already thinking id have to make the datapack from scratch, but ill gladly take and modify yours, thanks!
I love designs that look completely random from most perspectives until you stand in the right spot and suddenly it makes sense... I am contemplating trying to incorporate this into something I can build on our SMP now :D
I have never watched your channel before, but I'm sold on "baking tutorial for a cake you'll never bake". The pair of rings thumbnail was pretty great too (though a rainbow beacon thumbnail would have done the trick quite well).
going rainbow beacon would have been a nice throwback to the first video, woulda looked cool. though im glad i went with this, youtube seems to like it
It's like drawing an infinitely large 96-gon centered at (0,0), then drawing a line from the center to all 96 corners, then getting the minimum integer coordinates on that line outside a defined radius around (0,0)
The integer coordinates can only approximately touch the lines, cause most of the lines have irrational slopes, which means they never exactly hit any grid points except (0, 0)
@@HEHEHEIAMASUPAHSTARSAGA for 96ths of a circle i think a pretty decent portion if not most slopes are rational, still, you can just try to find the closest it gets to a block center within the specified radius
@@nddragoon I plugged the values into wolframalpha and it seems like all the slopes are irrational except the cardinal directions and diagonals (so 88 out of 96 are irrational). Though you can get arbitrarily close to any slope, it might require you to go out too far and make the beacon beam appear too small. It's an interesting question what the maximum allowed radius should be in order to make the effect look (subjectively) the best
i did a rainbow beacon in the past and wanted to make it a circle. It didn't look good due to the gaps between the beams as you explained, but i said it was acceptable since it was a single player world and no one would see this lol. I actually might reload this world and fix this rainbow beacon, to thank you for this video !
Title is partially clickbait. People assume, and rightly so, that a perfect circle refers to *world space* beacon placement when the author is talking about beacons in *screen space* (when looking up.)
@@MichaelPohoreski Yeah I was kinda expecting something like finding a best-fit radius for a 96-gon that's still fully loaded at once on a standard server. This was kinda neat anyway though.
you could probably consider how it'd look from the outside when deciding how much to space out the beacons and compromise a little bit on the size consistency without it mattering too much
i assumed the problem was that you couldn't place beacons next to each other or something lmao 😭 so, when you explained that it was actually that the spacing was uneven i thought it was a bit silly. BUT!!! i also completely understand the fun in solving random small problems like this so i quite enjoyed watching haha
I get the vibe that you have a passionate nerd rant (/pos) to go on about this, and I have never heard of this concept before and an so intrigued, care to explain? lmao
@@matchstick33 not really a rant, its just i find there is a specific style of doing things i always fall back to and maybe thats because im a really ptractical person who doesnt do any decorative stuff, so it 100% only has the functionality it needs to and nothing else, which i tend to describe as "warehouse", "factory" or "industrial" style. there isnt really a big thing behind it, also even if there was. its so long ago that i saw this video that i would probably not remember what my thought was anyways.
So excited this video has inspired my next two weeks of Minecraft obsession. I made a bunch of farms for beacons as my last project and then kinda stopped playing a few months back. Now I know what to do with all those beacons
This is really cool! The method you used very much reminds me of ray marching, which is typically used in rendering. It would only take a small tweak to the ray marching algorithm to turn it into a tool that does this automatically.
Oh yeah absolutely. Something I could try is spawning a shulker on each site and since shulkers snap to blocks, I can easily find the closest point to the center of the shulker
I feel like this kind of thing could almost be a numberphile video. This is a really cool lesson in perspective and why the idea of "perfection" is actually very subjective. Have you ever seen one of those sculptures that looks like a big chunk of nonsense, but shining a light on one side reveals that it casts a perfect shadow in the shape of a familiar object, and then shining a light at it from another angle casts a different shadow of a different familiar object? It's a fun way of playing with perspective. This video reminded me so much of that sort of thing. The way the circle looks careless and messy from almost any angle until you stand at the middle of the circle and it all organizes itself almost as if by magic, is genuinely an awesome thing to see play out. I love anything that can illustrate the extent to which perception can affected shape your ideas about "reality."
You know had you NOT pointed out the difference in spacing I might never have noticed but now its forever going to torture me. Thank god this video also handily fixes the issue you just pointed out.
"Perfection Within Chaos" I think this is a nice way to put this. Despite how messy things look from the outside, just by having a different perspective, looking from a different angle, suddenly, it all comes together beautifully… It also has a nice ring to it…
An interesting problem and a genius solution. You explained it all really well, kept it interesting, and the result was awesome (the warehouse light effect was a really nice touch). Great video all round!
this is quite interesting. and it may be possible to calculate and assign a score to different possible beacon placements based on 1. how close the of the beacon block is to the ideal angle line, and 2. how wide the apparent beacon beam is relative to the other beacon beams this is worth investigating, I'll have a look into it myself
Assigning scores would be a great solution instead of brute forcing! For closeness to the ideal line, it should decrease with distance, as differences in horizontal gaps would not be as noticeable at large distances I think. And for calculating apparent wideness vs other beams, you would need to know their sizes first to compare, which would make it recursive and weird. I think if you instead swap that for "distance to center", you would get the same effect, as beam width scales with radius! Really neat math problem overall, I wonder if there could be a formula that gives a more straight answer than just computing all the values and picking the best
@@ClaraDeLemonThis leads to a diophantine equation which is unfortunately NP-hard to solve in general. However, optimization isn't too hard via a branch / prune approach, and with this particular problem you can find good bounds fairly easily that exclude all but a small number of possibilities that can be easily checked
@@JPK314 It wouldn't be a diophantine equation, as the slopes of the straight lines are all irrational, and even then you dont want to find exact solutions, you want to find approximations, which is much easier to do than finding integer sols.
That’s awesome. While it wouldn’t be perfect, I think it might also be cool to simply increase the “thickness” of the circle, to have more beacons at each turn covering the gaps. Edit: actually this is a stupid idea cause you’d still have the same visible gaps between some of them unless it was extremely thick
@@vulpesinculta3478 to efficiently cover the gaps even more I think he would just need to plot more points the same way he did, but at a smaller turning increment
to increase the desnity you would have to increase the number of turns in the circle. Say you triple the number of turns, then you find 3 spots for each color (or you could have the colors repeat three times its up to the builder really). You would probably need a bigger radius to fit all of these beacons but I think this would increase the density better than making it thicker would.
@@rtrichterincreasing the number of turns would cause beacons to need to be placed even further to find ideal spots for them. While layering the beacons wouldn't have much variation in distance.
@@martinshoosterman layering the beacons at the same rotations wouldn't have any effect. Additionally layering them would require more distance as well. You need to find a second point along that ray that is close to an integer coordinate. When you stand in the middle that coordinate will just be behind the first beam (and since its farther away it will be smaller and completely invisible from the center). Layering them at a higher frequency decreases the distance between beams and therefore "covering the gaps" which is what OPs intention sounds like.
This was... Incredible. I'd love a block-by-block tutorial on how to build this exact setup (for those of us not savvy with commandblocks :)) and I already have a plan on where to include it, but I totally get if you want this to be a ”figure it out if you can, this was my project and i want it to stay that way” thing. This felt really cool and informative and for the first ever video I've watched from you, you gained another sub
Glad you enjoyed it! Theres a WDL for everything in the discord, and you can modify things to how you please. Theres also certain programs being used in the server so you could ask around if you want to use a computer to generate things instead.
I really like this style of video where you build something useful or fun and explain it. Tbh I couldn’t care less about how quickly you could destroy a hoe but would watch so much content if you explaining things like this or like the anvil launcher that was one of your first videos. More practical mechanisms, redstone or not, are far more interesting to watch, at least for me
i like your calmness, a lot of Minecraft content creators are so over exaggerating. But you Sir, you are just doing your thing and its interesting to watch
I feel like there's a maths dessertation somewhere in there. Like you just sort of brute forced this problem with a rotating armor-stand but I bet if an actual mathematician took a crack at it they would probably be able to deduce some sort of formula that approximates a circle on a square grid in this specific way. That's what fascinates me about yall redstoneheads, sometimes you guys just end up doing incredible maths recreationally and I think there's something quite pure and wholesome about that :3
I saw the title of this video and expected some sort of "Wifies" explanation type thing, and I don't usually get interested in those types of videos, however, I was really interested in your video by the way you conveyed things. You and Gneiss Name could be a good, underrated Minecraft duo, you earned a new subscriber.
yeah sure but this is not actually the angular difference. Both circles with diameter 34 and 35 can be built using 96 beacons. I'd go with 35 since i don't like double centers. you have 96 Blocks so your ideal Angular differences should be 360°/96 which is 3.75°. If you are in the middle of that circle and look south. The center of that block and the center of the block next to it have an angle of 3.37°, the next two enclose an angle of 3.34°, then 3.3° and then 3.23°, then when the first offset block comes the angle rises to 4.11°, 3.2°, 3.07°,4.44°,2.89°,4.57°,4.7°,4.76°, and then in reverse. The angles are all different.
I always love seeing one of your videos come out. They’re always so unique to most other people’s. And you explain things so well. You’ve come a long way since before you even had one thousand subscribers, not that long ago, but you’re still just as entertaining, if not more
Squiddy , this video has made me rethink my whole life , my wife came back , my son loves me again , my ex finally got over our breakup . Squirrel, there aren't words in the English language that can show my appreciation so I'ma just say - Thank you Pookiebear
OMG I’ve never heard a TH-camr use the slime rancher soundtrack in their videos before (which is honestly criminal bc it’s actually amazing)! Great vid ❤
This is a really interesting solution for this. My first thought was trying to find a paralell line in 3d space that would map to a target line in your view but your solution is very obvious, cutting straight into the problem with one insight that pops out when you think about it for more than 0 seconds.
interesting build! You mention how you rotate the armour stand 1/96th of a circle to find the next angle, but I don't think you mentioned where the armour stand starts facing. I would guess this would be directly North, South, East or West (a cardinal direction). All the potential blocks are directly aligned behind each other, so you have the least "wiggle room". I would guess that that this would make the best circle possible, but I might have written a code or done more maths to investigate further. You also don't explicitly mention where the the armour stand is located. I assume it is in the centre of the block as it appears to be. This would make sense given that the end portal is on a 1 block centre. However, I do wonder if a better result could be achieved by moving the centre. The problem I mentioned before of the blocks in cardinal direction being directly behind each other would be diminished if the centre were moved. Additionally, it is difficult to stand directly in the centre of a block, but if the player could align themselves in the centre (e.g. by walking into a corner), the player could stand in the exact centre, so perhaps get a better result. Sorry to be pedantic. I would like to reiterate that it already looks fab.
Bunch of great suggestions. Ill never be angry at someone who cares about the details. One possible approach for alignemnt is using a minecart and dismounting, perhaps you can eject one briefly out of the ground if it wasnt an end portal your circle was centered on. Imo cardinal directionn starting point makes most sense to me because anything else would make it REALLY hard to hit those exact cardinal direction beams
Since 96/4 is 14, it should be that every 24 increments the armour stand will point in a cardinal direction anyway, so it wouldn't matter which cardinal direction you stared with. Having some alignment method would be useful, but I'd think just using a minecart would work perfectly fine. Having each 24 increments result in a perfect 90 degree turn means that you only need to solve for those 24 increments, and afterward copy the pattern to the other four quadrants. In fact, since you can divide everything into 8 lots of 12, you can solve for the first 12 increments, mirror the solution across the next eighth, then copy the resulting quarter across the other four quadrants. Then you can put more effort into making the best compromise between smallest deviation from the 1/96th increment turns and the deviation from the overall circle. As part of that process I'd also recommend putting multiple targets down for each increment, marking each block that's within an acceptable margin of the ray. Then afterwards, choose all the targets that have minimum deviation from a circle.
@@squibble111 Alternatively, you could do the calculations outside of minecraft - write a python script or something that finds the set of 96 equally spaced rays that, for a center location either on a grid point or at a half-unit offset, get on average the closest to a gridpoint within a given range of radii. And then just output that as a list of coordinate offsets for where the beacons go.
@@patrickhector "it wouldn't matter which cardinal direction you stared with" that isn't at all what i meant. If you started 1/192nd of a revolution from north, and went in 1/96th increments, then the armour stand would never point in a cardinal direction. On your next point: In the case of starting in a cardinal direction, you might have to pick the block for thirteen directions. (The diagonals and the cardinal directions will be shared between the eighths). If not starting in a cardinal direction, then mirroring will not work, so you can only use the order-4 rotational symmetry.
the ingenuity here is incredible, seeing the problem and deciding there must be a way to solve it instead of decrying it as a 'quirk of minecraft' is incredible
I was expecting some complicated maths to find the optimal arrangement - the use of the armour stand is a very satisfying way to solve the problem. Well done :)
I really like the armor stand raycast. The resulting effect is really cool. I like the effect from places slightly off center, where they're not perfectly aligned but there's not an obvious grid pattern
the second u faced the camera upwards, i got it, i dont want no explanation, i dont understand why it happens but the fact that it works blows my mind and i wanna keep it that way, liked and subbed tho, great content!
Yeah me too, I was wandering what is the rule. It can't be the ratio of eg. yellow to orange, so it has to be some counter of intensity. I am curious now how it works exactly.
it definitely would not look good from the inside, those regions with less "beacon density" than the cardinal directions would now have more "beacon density" than the cardinal directions and you're left with the same issue
That video and the color grading one actually helped on the end barrens I were trying to convert each discovered island in a gimmick and the island that i woulf focus on beacon messed me up when i tried to make bigger circles with degrade Thanks, hope you get even more recognization
This could've been solved mathematically instead of experimentally! What you're effectively doing is trying to find good rational approximations of various irrationals. What you want to do is subdivide a circle into 96 evenly spaced units (for the 96 beacon colours), meaning each turn (such as for your armour stand) is 3.75 degrees. You have two conflicting requirements here, that are probably best expressed via a triangle. - You want to draw a right angled triangle with an angle (theta) as close as possible to each of those 3.75 degree increments - The hypotenuse of each triangle (aka radius of the circle) must be roughly equal (that is to say, you don't a drastically difference between each beacon; you want to find integers that are in the same ballpark) Additionally, the width and height of this triangle must be integers (since it's in minecraft, they're snapped to an integer grid) A standard "minecraft circle" is one that only cares about a consistent radius (hypotenuse). You care much more about there being a consistent 3.75 degrees between each beam. This is a mathematical approach to the experimental solution you found using the armour stand and raycasting, which can be generalised to many use-cases. You also only need to do 1/8th of a full circle, as you can mirror that to get a quarter-circle, and rotate that around to get the full thing. This means that instead of 96 coordinate pairs, you only really need to find 12 (well, 13, fenceposting for the diagonal). Starting from 0 degrees, and increasing 3.75 degrees each time, until you reach 45 degrees. To convert a degree angle into a pair of coordinates (let's use 30 degrees for example) you would have to convert it to radians (0.523598776...) and then find the tangent of that (0.577350269...). This gives you a decimal value (that's not necessarily rational). What you want is a rational (fractional) approximation of this value. Minecraft blocks are locked to an integer coordinate grid, which means you can only move a whole number of blocks in each direction. Obviously 5773/10000 would be a decent approximation of 0.5773, which would correspond to placing a beacon at the coordinate (5773, 10000). However that would place the beacon over 10,000 blocks away, well outside render distance, which isn't the best for visibility... also, we can get better approximations. You want to keep the denominator of this ratio relatively low, while maintaining as much accuracy as possible. For this, you can use a Farey sequence, implementing a Continued Fraction algorithm (google those terms for more info). These algorithms tell us that fractions such as 4/7 and 11/19 are good approximations of our 0.5773... decimal. We can check these with a trig calculator (omnicalculator has a good one) - plug in those values for the height and width of a triangle, and see that it has an angle pretty close to our target of 30 degrees. If we draw this visually, we can see how accurate it really is; i.imgur.com/LX8fsZz.png You say that this information is useful to almost nobody, but it's the opposite! What you're seeking by asking this question is something incredibly useful, and was a question asked by Euclid, around 2300 years ago! If you've ever used 22/7 as an approximation for pi, this is the branch of mathematics you have to thank for it.
the distance between 2 beacons is 1 block, the distance between 2 diagonal beacons is 1.4 blocks. if you find a way to move the beacons to be 1.4 blocks away from each other when placed one next to the other you'll fix the issue. 1 & 1.4 → 10 & 14 → 5 & 7 hypothetically, if you place a beacon every 7 blocks vertically and 5 blocks diagonally, it will fix the issue of spaces. the circle will end up a lot bigger but eh. edit: I tried it, I accidentally did a 6/4 instead of a 7/5, it ended up pretty big but still in render distance from the center, and it looks awesome! definitely gonna add it to a megabase someday
Cake you won't bake is a perfect analogy lol. Very small difference but a noticable one. I thought this might be about effect area usefulness but colors are pretty cool too. Good video!
Holy moly you are an absolute genius, love ur videos, they're always not only interesting, but explained in enough depth to make even a layman like me understand the concept!! :D
![ลองสุ่มไอโฟน 990 โกงมั้ย? [ โกงมั้ยครับ ep.101 ] | DOM](http://i.ytimg.com/vi/bfsWe0j492k/mqdefault.jpg)
I actually like the fact that it looks very random from the outside, but when you stand on the center block it becomes a perfect circle. I really like chaotic designs like this and having them come together so beautifully is wonderful. I must build this in my hardcore world!
ill post the schematic of both the world and the armor stand tols in the schem channel in my discord, if you want to take it, or possibly make your own (if you have a bigger gradient)
@@squibble111 how would you get a bigger gradient? Isn't 5 glass blocks the max?
@@kr1vthere are FAR more permutations than just these 96
@@kr1v you could switch between more colors. He didn't include the values or brown. You could also reuse colors in your gradient, or do something crazy with mixing 3 colors at once
@@squibble111 I was thinking of making a muuuuch bigger circle for one of the farms im cooking and I was already thinking id have to make the datapack from scratch, but ill gladly take and modify yours, thanks!
0:43 "A baking tutorial for a cake you'll never bake" *Awkwardly turns to see my collection of recipe books*
You're not obligated to make every recipe in every cookbook
@@quantumblur_3145 Heresy
Wysi likes
Osusosuusousosus@@Aerolite_FPSwysi 727 wysi !!!!!
No but same-
you actually found a solution for the problem im trying to solve since half a year
congratulations on being the single member of the uninentionally targeted audience
It can easily be done with some trig tho
@@itripleo5780nerd
@@itripleo5780 Hush, mathematics graduate
Do the trig and get us a graph of it @@itripleo5780
I love designs that look completely random from most perspectives until you stand in the right spot and suddenly it makes sense... I am contemplating trying to incorporate this into something I can build on our SMP now :D
its like those pictures made out of lots of hanging objects. they are so cool!
copy pasta 😜
accidental?
@@kipu44 oh my god, two people that have a similar opinion! How could that happen??? Drama!!
@@IMadeAnEntireSpeciesForWhatyou mean like Squibble's perspective art? :D th-cam.com/video/RUBg41KUs2I/w-d-xo.htmlsi=pMjevp67jfdVtPc8
@@kipu44OH MY GOD, PEOPLE HAVE THE SAME OPINION??? HOW WILD!!!
I have never watched your channel before, but I'm sold on "baking tutorial for a cake you'll never bake". The pair of rings thumbnail was pretty great too (though a rainbow beacon thumbnail would have done the trick quite well).
going rainbow beacon would have been a nice throwback to the first video, woulda looked cool. though im glad i went with this, youtube seems to like it
@@squibble111 it definitely creates the contrary assertion that brings in the clicks. But also, you deliver on it!
@@squibble111 yeah, i like that simple and technical thumbnail so it really got my attention
@@squibble111the thumbnail definitely pulled me in from the main page so i say its working
i probab;y wouldnt have watched if it was just a tutorial onb how to do that. ig why i clicked is the why behind the given diagrams. good video
Gives the same vibe as those art pieces that are loads of bits on strings but forms a coherent picture when viewed at a specific angle
It's like drawing an infinitely large 96-gon centered at (0,0), then drawing a line from the center to all 96 corners, then getting the minimum integer coordinates on that line outside a defined radius around (0,0)
The integer coordinates can only approximately touch the lines, cause most of the lines have irrational slopes, which means they never exactly hit any grid points except (0, 0)
doesn't even have to be infinitely large, it can just be big enough that the beacons all fit inside. There's definitely a way to automate this
@@HEHEHEIAMASUPAHSTARSAGA for 96ths of a circle i think a pretty decent portion if not most slopes are rational, still, you can just try to find the closest it gets to a block center within the specified radius
@@HEHEHEIAMASUPAHSTARSAGAAlthough they do get arbitrarily close, if you go out far enough
@@nddragoon I plugged the values into wolframalpha and it seems like all the slopes are irrational except the cardinal directions and diagonals (so 88 out of 96 are irrational). Though you can get arbitrarily close to any slope, it might require you to go out too far and make the beacon beam appear too small. It's an interesting question what the maximum allowed radius should be in order to make the effect look (subjectively) the best
i did a rainbow beacon in the past and wanted to make it a circle. It didn't look good due to the gaps between the beams as you explained, but i said it was acceptable since it was a single player world and no one would see this lol. I actually might reload this world and fix this rainbow beacon, to thank you for this video !
Looks considerably better from the inside than outside, maybe thats it.
Like the Tardis. 😁
Title is partially clickbait. People assume, and rightly so, that a perfect circle refers to *world space* beacon placement when the author is talking about beacons in *screen space* (when looking up.)
@@MichaelPohoreski Yeah I was kinda expecting something like finding a best-fit radius for a 96-gon that's still fully loaded at once on a standard server. This was kinda neat anyway though.
you could probably consider how it'd look from the outside when deciding how much to space out the beacons and compromise a little bit on the size consistency without it mattering too much
@@MichaelPohoreskiwell yeah people should know that's impossible in a cube grid game
i assumed the problem was that you couldn't place beacons next to each other or something lmao 😭
so, when you explained that it was actually that the spacing was uneven i thought it was a bit silly.
BUT!!! i also completely understand the fun in solving random small problems like this so i quite enjoyed watching haha
same 😅
Same here! Turns out it was a very neat perspective puzzle.
this blew my mind
omg it's crafty
blows up pancakes with mind
Dirt blocks have low explosion resistance, so that makes sense
omg its crafter counter
cop flop > crafty counter
so the conclusion is that warehouse style is the best approach to almost anything.
I get the vibe that you have a passionate nerd rant (/pos) to go on about this, and I have never heard of this concept before and an so intrigued, care to explain? lmao
@@matchstick33 not really a rant, its just i find there is a specific style of doing things i always fall back to and maybe thats because im a really ptractical person who doesnt do any decorative stuff, so it 100% only has the functionality it needs to and nothing else, which i tend to describe as "warehouse", "factory" or "industrial" style. there isnt really a big thing behind it, also even if there was. its so long ago that i saw this video that i would probably not remember what my thought was anyways.
So excited this video has inspired my next two weeks of Minecraft obsession. I made a bunch of farms for beacons as my last project and then kinda stopped playing a few months back. Now I know what to do with all those beacons
3:24 that is actually gorgeous
It looks like a star
This is really cool! The method you used very much reminds me of ray marching, which is typically used in rendering. It would only take a small tweak to the ray marching algorithm to turn it into a tool that does this automatically.
Oh yeah absolutely. Something I could try is spawning a shulker on each site and since shulkers snap to blocks, I can easily find the closest point to the center of the shulker
I feel like this kind of thing could almost be a numberphile video. This is a really cool lesson in perspective and why the idea of "perfection" is actually very subjective. Have you ever seen one of those sculptures that looks like a big chunk of nonsense, but shining a light on one side reveals that it casts a perfect shadow in the shape of a familiar object, and then shining a light at it from another angle casts a different shadow of a different familiar object? It's a fun way of playing with perspective. This video reminded me so much of that sort of thing.
The way the circle looks careless and messy from almost any angle until you stand at the middle of the circle and it all organizes itself almost as if by magic, is genuinely an awesome thing to see play out.
I love anything that can illustrate the extent to which perception can affected shape your ideas about "reality."
Absolutely agree. The subjectivity of perspective is a fascinating topic in general, and one that spans multiple fields of study
You know had you NOT pointed out the difference in spacing I might never have noticed but now its forever going to torture me. Thank god this video also handily fixes the issue you just pointed out.
"Perfection Within Chaos"
I think this is a nice way to put this. Despite how messy things look from the outside, just by having a different perspective, looking from a different angle, suddenly, it all comes together beautifully…
It also has a nice ring to it…
NOOOO sqrt 2 stikes again... disgusting irrationals. we must embrace hexagons
Hexagons, embeded with sqrts(3) all over the place...
@@Faroshkasb- but hexagons are the bestagons..
@@gallium-gonzollium even the bestagons betray us
sqrt 5 : (sad)
@@nartoomeon9378golden ratio!! :3 pentagons :333
An interesting problem and a genius solution. You explained it all really well, kept it interesting, and the result was awesome (the warehouse light effect was a really nice touch). Great video all round!
Thank you !
this is quite interesting. and it may be possible to calculate and assign a score to different possible beacon placements based on 1. how close the of the beacon block is to the ideal angle line, and 2. how wide the apparent beacon beam is relative to the other beacon beams
this is worth investigating, I'll have a look into it myself
Ooh, that would be really cool to design a program to do that! if you do come up with sometihing please do let me know on the discord server
Assigning scores would be a great solution instead of brute forcing! For closeness to the ideal line, it should decrease with distance, as differences in horizontal gaps would not be as noticeable at large distances I think. And for calculating apparent wideness vs other beams, you would need to know their sizes first to compare, which would make it recursive and weird. I think if you instead swap that for "distance to center", you would get the same effect, as beam width scales with radius!
Really neat math problem overall, I wonder if there could be a formula that gives a more straight answer than just computing all the values and picking the best
@@ClaraDeLemonThis leads to a diophantine equation which is unfortunately NP-hard to solve in general. However, optimization isn't too hard via a branch / prune approach, and with this particular problem you can find good bounds fairly easily that exclude all but a small number of possibilities that can be easily checked
@@JPK314 It wouldn't be a diophantine equation, as the slopes of the straight lines are all irrational, and even then you dont want to find exact solutions, you want to find approximations, which is much easier to do than finding integer sols.
@@squibble111sry for the ping, but has someone come up with something? if not, i will try something, but first want to know, that it isn't solved yet
Aperture Beacon Science tm
What I learned instead is that no two men's OCD is the same
Having ocd of that sane thing
Зинаида?!
cooking tutorials for dishes ill never make are the only possible cooking tutorials for me
That’s awesome. While it wouldn’t be perfect, I think it might also be cool to simply increase the “thickness” of the circle, to have more beacons at each turn covering the gaps.
Edit: actually this is a stupid idea cause you’d still have the same visible gaps between some of them unless it was extremely thick
Perhaps if it is layered thrice? Though maybe it would need more.
@@vulpesinculta3478 to efficiently cover the gaps even more I think he would just need to plot more points the same way he did, but at a smaller turning increment
to increase the desnity you would have to increase the number of turns in the circle. Say you triple the number of turns, then you find 3 spots for each color (or you could have the colors repeat three times its up to the builder really). You would probably need a bigger radius to fit all of these beacons but I think this would increase the density better than making it thicker would.
@@rtrichterincreasing the number of turns would cause beacons to need to be placed even further to find ideal spots for them.
While layering the beacons wouldn't have much variation in distance.
@@martinshoosterman layering the beacons at the same rotations wouldn't have any effect. Additionally layering them would require more distance as well. You need to find a second point along that ray that is close to an integer coordinate. When you stand in the middle that coordinate will just be behind the first beam (and since its farther away it will be smaller and completely invisible from the center). Layering them at a higher frequency decreases the distance between beams and therefore "covering the gaps" which is what OPs intention sounds like.
This was... Incredible. I'd love a block-by-block tutorial on how to build this exact setup (for those of us not savvy with commandblocks :)) and I already have a plan on where to include it, but I totally get if you want this to be a ”figure it out if you can, this was my project and i want it to stay that way” thing. This felt really cool and informative and for the first ever video I've watched from you, you gained another sub
Glad you enjoyed it! Theres a WDL for everything in the discord, and you can modify things to how you please. Theres also certain programs being used in the server so you could ask around if you want to use a computer to generate things instead.
It’s an anamorphic piece of art really. You’ve overcome a technical limitation to create something circular in a square world.
I really like how it looks like you could put in a natural path to travel to the inside/outside of the circle, too, which I really like.
I really like this style of video where you build something useful or fun and explain it. Tbh I couldn’t care less about how quickly you could destroy a hoe but would watch so much content if you explaining things like this or like the anvil launcher that was one of your first videos. More practical mechanisms, redstone or not, are far more interesting to watch, at least for me
You've made something incredibly epic here.
I immediately recognized the Smile Rancher ruin music too so that's awesome as well
Gotta love how the perfect circle looks like a starting position for Conway's Game of Life.
i like your calmness, a lot of Minecraft content creators are so over exaggerating.
But you Sir, you are just doing your thing and its interesting to watch
Very cool. Quite interesting that it looks completely random by an outside observer, but looks fantastic and evenly-spaced on the inside. Great job!
I feel like there's a maths dessertation somewhere in there. Like you just sort of brute forced this problem with a rotating armor-stand but I bet if an actual mathematician took a crack at it they would probably be able to deduce some sort of formula that approximates a circle on a square grid in this specific way. That's what fascinates me about yall redstoneheads, sometimes you guys just end up doing incredible maths recreationally and I think there's something quite pure and wholesome about that :3
I saw the title of this video and expected some sort of "Wifies" explanation type thing, and I don't usually get interested in those types of videos, however, I was really interested in your video by the way you conveyed things. You and Gneiss Name could be a good, underrated Minecraft duo, you earned a new subscriber.
Thank you, im honored to be batched into the same group as the great gneiss name
The slime rancher hits different
This is something I’d likely never build, but is genuinely so cool that I can’t help but admire it.
the diagonal distance is sqrt(2), which is 41% bigger than beacons just next to each other. You can calculate the distance using Pythagoras' theorem.
yeah sure but this is not actually the angular difference. Both circles with diameter 34 and 35 can be built using 96 beacons. I'd go with 35 since i don't like double centers. you have 96 Blocks so your ideal Angular differences should be 360°/96 which is 3.75°. If you are in the middle of that circle and look south. The center of that block and the center of the block next to it have an angle of 3.37°, the next two enclose an angle of 3.34°, then 3.3° and then 3.23°, then when the first offset block comes the angle rises to 4.11°, 3.2°, 3.07°,4.44°,2.89°,4.57°,4.7°,4.76°, and then in reverse. The angles are all different.
This is such a good video. Super clever technique of approximating the best spots and a super clever solution I would have never thought of!
God damn I hope you’re an engineer irl bc this is really smart. The second I saw how you used the armor stand I was like this guy is a genius.
I always love seeing one of your videos come out. They’re always so unique to most other people’s. And you explain things so well. You’ve come a long way since before you even had one thousand subscribers, not that long ago, but you’re still just as entertaining, if not more
Thank you for the compliment. I appreciate you having been here since then, the channel's definitely come a long way
Squiddy , this video has made me rethink my whole life , my wife came back , my son loves me again , my ex finally got over our breakup . Squirrel, there aren't words in the English language that can show my appreciation so I'ma just say - Thank you Pookiebear
I’d recognize that music from anywhere It tickles my brain with nostalgia
A far far away life 😌
OMG I’ve never heard a TH-camr use the slime rancher soundtrack in their videos before (which is honestly criminal bc it’s actually amazing)! Great vid ❤
The most unexpected song you can hear in a Minecraft video is a Slime Rancher theme to be honest
whats also surprising is the disproportionately large amount of rain world fans who watch my videos. i don't know where they all come from
This is a really interesting solution for this. My first thought was trying to find a paralell line in 3d space that would map to a target line in your view but your solution is very obvious, cutting straight into the problem with one insight that pops out when you think about it for more than 0 seconds.
interesting build!
You mention how you rotate the armour stand 1/96th of a circle to find the next angle, but I don't think you mentioned where the armour stand starts facing.
I would guess this would be directly North, South, East or West (a cardinal direction). All the potential blocks are directly aligned behind each other, so you have the least "wiggle room".
I would guess that that this would make the best circle possible, but I might have written a code or done more maths to investigate further.
You also don't explicitly mention where the the armour stand is located. I assume it is in the centre of the block as it appears to be. This would make sense given that the end portal is on a 1 block centre.
However, I do wonder if a better result could be achieved by moving the centre. The problem I mentioned before of the blocks in cardinal direction being directly behind each other would be diminished if the centre were moved. Additionally, it is difficult to stand directly in the centre of a block, but if the player could align themselves in the centre (e.g. by walking into a corner), the player could stand in the exact centre, so perhaps get a better result.
Sorry to be pedantic. I would like to reiterate that it already looks fab.
Bunch of great suggestions. Ill never be angry at someone who cares about the details. One possible approach for alignemnt is using a minecart and dismounting, perhaps you can eject one briefly out of the ground if it wasnt an end portal your circle was centered on. Imo cardinal directionn starting point makes most sense to me because anything else would make it REALLY hard to hit those exact cardinal direction beams
Since 96/4 is 14, it should be that every 24 increments the armour stand will point in a cardinal direction anyway, so it wouldn't matter which cardinal direction you stared with. Having some alignment method would be useful, but I'd think just using a minecart would work perfectly fine. Having each 24 increments result in a perfect 90 degree turn means that you only need to solve for those 24 increments, and afterward copy the pattern to the other four quadrants. In fact, since you can divide everything into 8 lots of 12, you can solve for the first 12 increments, mirror the solution across the next eighth, then copy the resulting quarter across the other four quadrants. Then you can put more effort into making the best compromise between smallest deviation from the 1/96th increment turns and the deviation from the overall circle.
As part of that process I'd also recommend putting multiple targets down for each increment, marking each block that's within an acceptable margin of the ray. Then afterwards, choose all the targets that have minimum deviation from a circle.
@@squibble111 Alternatively, you could do the calculations outside of minecraft - write a python script or something that finds the set of 96 equally spaced rays that, for a center location either on a grid point or at a half-unit offset, get on average the closest to a gridpoint within a given range of radii. And then just output that as a list of coordinate offsets for where the beacons go.
@@patrickhector "it wouldn't matter which cardinal direction you stared with" that isn't at all what i meant. If you started 1/192nd of a revolution from north, and went in 1/96th increments, then the armour stand would never point in a cardinal direction.
On your next point: In the case of starting in a cardinal direction, you might have to pick the block for thirteen directions. (The diagonals and the cardinal directions will be shared between the eighths). If not starting in a cardinal direction, then mirroring will not work, so you can only use the order-4 rotational symmetry.
the ingenuity here is incredible, seeing the problem and deciding there must be a way to solve it instead of decrying it as a 'quirk of minecraft' is incredible
nice to see I'm not the only one who figured out the right glass pattern for a good rainbow
This is a very smart and accurate solution to the problem. I have already built a beacon circle before, but i haven't thought about this problem.
Splendid choice of music :)
hi bronkulator
I was expecting some complicated maths to find the optimal arrangement - the use of the armour stand is a very satisfying way to solve the problem. Well done :)
Such a neat problem. Awesome video
Amazing video! Love how you explained how you came up with the shape
omgg u have a little lantern hat :3
I really like the armor stand raycast. The resulting effect is really cool. I like the effect from places slightly off center, where they're not perfectly aligned but there's not an obvious grid pattern
7:56 "but, *in the end* ..."
it doesn't even matter...
but in the end...
it doesn’t even matter…
the second u faced the camera upwards, i got it, i dont want no explanation, i dont understand why it happens but the fact that it works blows my mind and i wanna keep it that way, liked and subbed tho, great content!
You just made ray marching in Minecraft... for a beacon. You're channel never fails to blow my mind
I'm admiring the fact that it looks chaotic until you stand in the middle and it all looks perfect.
Mom: Your OCD isn’t that bad
Me: … I need the beacon beams mathematically perfectly apart.
A baking tutorial for a cake you'll never bake is a fire line
loved this whole concept but WOW that redstone circuit at the end was so cool, i have to do that for a build some day
I think this video explains why you can't make the perfect circle in Minecraft :}
You are right, I will probably never build this, but you made me want to and that sir is a success in my book.
ah, yes, the slime rancher music :D
Best thing to watch at 2am while having a mental brakedown. I'll 100% use this in my survival world when I get better
2:15 what is this shader, ive seen this end effect so many times now. What is it?!?!?
looks like complementary reimagined
I love how you overdid this but I literally can't see a difference between the two LOLLL
7:30 I can see binary counter here)
Yeah me too, I was wandering what is the rule. It can't be the ratio of eg. yellow to orange, so it has to be some counter of intensity. I am curious now how it works exactly.
Not exactly binary but true
Waiting for an “End” counter for the amount of times you said “End” or variants of that word like “Ends.”
I think filling in all of the corners of the original circle would help a lot and would still look good from the outside
it definitely would not look good from the inside, those regions with less "beacon density" than the cardinal directions would now have more "beacon density" than the cardinal directions and you're left with the same issue
Thank you, you've reignited the dying flame that was my monthly minecraft phase.
You cant because it is a game with cubes.
i think he is aware that this game contains cubes
NUH UH
You can because it's a sandbox game
@@costa-w3k i found no sandboxes in this sandbox game 0/10
@@dirtydan3029suspicious sand stores stuff like a box,10/10
the fact that this guy made a video full of almost completely useless information yet kept me entertained is incredible
You said no one is going to make it, so just because of that Im going to make one.
if you want the armor stand doohickey itll probbaly be in the discord server in a bit
I love the off and on sequence, it’s like a light show
"Why you can't make a Perfect Circle with Beacons in Minecraft" 2:49 THATS LITERALLY A PERFECT CIRCLE WITH BEACONS IN MINECRAFT
Tell me you didn't watch the full video without watching the full video
Why is this making feel so nostalgic, I think its his voice it fits the old calming Minecraft videos back in the day.
That video and the color grading one actually helped on the end barrens
I were trying to convert each discovered island in a gimmick and the island that i woulf focus on beacon messed me up when i tried to make bigger circles with degrade
Thanks, hope you get even more recognization
This could've been solved mathematically instead of experimentally! What you're effectively doing is trying to find good rational approximations of various irrationals.
What you want to do is subdivide a circle into 96 evenly spaced units (for the 96 beacon colours), meaning each turn (such as for your armour stand) is 3.75 degrees. You have two conflicting requirements here, that are probably best expressed via a triangle.
- You want to draw a right angled triangle with an angle (theta) as close as possible to each of those 3.75 degree increments
- The hypotenuse of each triangle (aka radius of the circle) must be roughly equal (that is to say, you don't a drastically difference between each beacon; you want to find integers that are in the same ballpark)
Additionally, the width and height of this triangle must be integers (since it's in minecraft, they're snapped to an integer grid)
A standard "minecraft circle" is one that only cares about a consistent radius (hypotenuse). You care much more about there being a consistent 3.75 degrees between each beam. This is a mathematical approach to the experimental solution you found using the armour stand and raycasting, which can be generalised to many use-cases.
You also only need to do 1/8th of a full circle, as you can mirror that to get a quarter-circle, and rotate that around to get the full thing. This means that instead of 96 coordinate pairs, you only really need to find 12 (well, 13, fenceposting for the diagonal). Starting from 0 degrees, and increasing 3.75 degrees each time, until you reach 45 degrees.
To convert a degree angle into a pair of coordinates (let's use 30 degrees for example) you would have to convert it to radians (0.523598776...) and then find the tangent of that (0.577350269...). This gives you a decimal value (that's not necessarily rational). What you want is a rational (fractional) approximation of this value. Minecraft blocks are locked to an integer coordinate grid, which means you can only move a whole number of blocks in each direction. Obviously 5773/10000 would be a decent approximation of 0.5773, which would correspond to placing a beacon at the coordinate (5773, 10000). However that would place the beacon over 10,000 blocks away, well outside render distance, which isn't the best for visibility... also, we can get better approximations. You want to keep the denominator of this ratio relatively low, while maintaining as much accuracy as possible.
For this, you can use a Farey sequence, implementing a Continued Fraction algorithm (google those terms for more info). These algorithms tell us that fractions such as 4/7 and 11/19 are good approximations of our 0.5773... decimal. We can check these with a trig calculator (omnicalculator has a good one) - plug in those values for the height and width of a triangle, and see that it has an angle pretty close to our target of 30 degrees.
If we draw this visually, we can see how accurate it really is; i.imgur.com/LX8fsZz.png
You say that this information is useful to almost nobody, but it's the opposite! What you're seeking by asking this question is something incredibly useful, and was a question asked by Euclid, around 2300 years ago! If you've ever used 22/7 as an approximation for pi, this is the branch of mathematics you have to thank for it.
I actually like the rainbow glass without the beacons too looks like some cool colourful crystals
this is SO FREAKING COOL wow that solution with the armor stand is so fascinating
this is so beautifully overengineered
the distance between 2 beacons is 1 block, the distance between 2 diagonal beacons is 1.4 blocks. if you find a way to move the beacons to be 1.4 blocks away from each other when placed one next to the other you'll fix the issue.
1 & 1.4 → 10 & 14 → 5 & 7
hypothetically, if you place a beacon every 7 blocks vertically and 5 blocks diagonally, it will fix the issue of spaces. the circle will end up a lot bigger but eh.
edit: I tried it, I accidentally did a 6/4 instead of a 7/5, it ended up pretty big but still in render distance from the center, and it looks awesome! definitely gonna add it to a megabase someday
Dude u have made the PERFECT thumbnail 😧 i always keep clicking on this video no matter how many times i have seen it in my recommended. Good job
This is the most fascinating bit of information I will probably never need
Cake you won't bake is a perfect analogy lol. Very small difference but a noticable one. I thought this might be about effect area usefulness but colors are pretty cool too. Good video!
"It's best to consider this a baking tutorial for a cake you'll never bake" is unexpectedly poetic
As Kendrick once said
"A perfect circle's never perfect only filled with lies"
Very deep conceptual lyrics.
that's the amazing fusion of creativity an technicalities, that I love about this game. Thanks for sharing this with me!
That was awesome! Love how it all comes together in the end.
Holy moly you are an absolute genius, love ur videos, they're always not only interesting, but explained in enough depth to make even a layman like me understand the concept!! :D
I don’t usually watch much minecraft content but I’m glad I watched this. You are very talented, I love your building style
Why do I feel like this is a Mysticat video waiting to happen?
You solved this problem nobody had perfectly. This is neat
i actually needed this for my server with some friends, thanks!
your skybox and shaders look absolutely beautiful
Pretty elegant solution! no complex programming, math, or website to template!
This is how I'd imagine a 4th dimensional tutorial video to be like with the abstract circle