How to Build a Julia Set
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- เผยแพร่เมื่อ 30 ก.ค. 2024
- In this video we examine how to build a Julia Set by making repeated remapping of a circle on the complex plane. The technique is quite interesting because it allow us to visually understand why Julia Sets have some of their properties, such as rotational symmetry. This video only glosses over the mathematics, and don't worry if you don't exactly understand what is going on. The important part is to look at Julia Set being formed visually. I'm certainly not the first to use this technique, but there isn't much TH-cam content, so I've included quite a few visuals, and everything is rendered at a super high 8k resolution. Consider playing the final visuals at slower speeds if you wish to study them. Please subscribe!
If you loved this video then why not buy me a coffee: ko-fi.com/mathstown
In this series:
1 - • The Mandelbrot Set Exp... The Mandelbrot Set Explained
2 - • Julia Sets, and how th... Julia Sets, and how they relate to The Mandelbrot Set
3 - • How to Build a Julia Set How to Build a Julia Set
4 - • Number Sequences in th... Number Sequences in the Mandelbrot Set
Extra Visuals (No commentary):
• [Extra Visual] All orb... - All orbits of the Mandelbrot
• [Extra Visual] All Per... - Period 1 orbits of the Mandelbrot
• [Extra Visual] All Per... - Period 2 orbits of the Mandelbrot
• [Extra Visual] Buildin... - Building a Mandelbrot step-by-step
• [Extra Visual] Period ... - Period 2 orbits of a Julia Set
• [Extra Visual] Period ... - Period 3 orbits of a Julia Set
• [Extra Visual] Period ... - Period 4 orbits of a Julia Set
• [Extra Visual] Period ... - Period 5 orbits of a Julia Set
• [Extra Visual] Period ... - Period 6 orbits of a Julia Set
This page offered some inspiration for this video: www.karlsims.com/julia.html
Fascinating. After seeing your videos i understand why mathematicians often say that math is art.
An interesting point not stated in the video: For disconnected Julia sets, the point of iteration when building it when the set "breaks up" is the same iteration where the corresponding point (not) in the Mandelbrot set goes out of bounds. For the set at the end, it will take another 50 or so iterations for the set to become disconnected, though it would be hard to tell without zooming in.
Sir this is pure gold, I feel lucky to be among 5325 lucky viewers of your art
Also question, I feel like that there is at least some points on Mandelbrot's set edge that are essentially "true points", as infinetely thin connecting bridges between different parts of set, so do we know where they are (analitically) and understand, what they mean? Probably set of those points is somehow "higher order" fractal than Mandelbrot's?
edit: or probably that fractal essentially converges to the edge of Mandelbrot's..
Yes, there are infinity thin points. We know where some, but not all, connect (for example where bulbs connect to cardioid, see next video). There are also the branch the points of the antennas, which are infinity 'similar' and thin.
I appreciate the effort you've put into all of these videos. I've always wanted to learn more about fractals, and these presentations do an incredible job of being both informative and just plain fun to watch. Thank you for sharing!
I was so surprised you only have 900 subscribers, this video is awesome keep it up!
Whoa I didn’t even notice lol! This page is on the edge of blowing up probably
Amazing! This is a gem channel!
Thank-you. I appreciate the kind words.
best video of julia set explanation on youtube! thanks man, you reallu made my life easier. instant like
Thank you for this video, it made it kinda easier to understand how does this actually work!
This is very insightful: Mandelbrot is a mere study of the 0+0.i point of julia set "c". And the inverse julia set construction showing how the fractal is formed.
Excellent.
Your still dummy ing it lol.
You should have also done a Julia set for a Misiurewicz point, such as c = I.
Fantastically helpful
Does the example that ends at 14:16 ever break apart? It feels like it's always closer and closer to exploding into dust
Yes, it is actually already broken at the timestamp you indicated. You can probably see if you look very closely at the centre (0,0). It will hold its overall form, but the bits get thinner and thinner as you iterate. It will take about 800 iterations to fade from the screen (I just checked).
@Tagliaferri Andrea program i think????
Great job
11:50
Therapist: Snake JUlia doesnt exist, it cant hurt you.
*Snake Julia:*
My favorite Julia set is the last part. And the disconectted Julia is called the Fauto Dust
Why is the equation z=z^2+c so unique and not z=z^3+c or z^4 etc. and what happens when z is raised to a different power? Does it make a shape and are they usable? Too much chaos?
Is there a correlation between how everything past 2 or -2 goes off towards infinity because z is being squared vs if it was being raised to say the 3rd power would the points start to go toward infinity if they were outside 3 or -3?
Thanks for all the educational and visually impressive videos!
Can confirm if this understanding of difference between Mandelbrot and Julia shader calculations is correct?:
Main difference is seemingly that a Mandelbrot set has a C val that changes every pixel as it basically seems to do a “for loop” style scan across each row of texture coordinates row by row in the entire frame.
So at each point it is calculating the pixel color for, it inputs that texture coordinate under that pixel as C.
In a julia set Z is initially set to the texture coordinate it’s rendering the pixel color for, but C is a constant coordinate val that is shared by every pixel (texture coordinate under the pixel) calculation and that val is from a specified n+i plane coordinate selected. (so in an interactive shader, the coordinate under the touch is C and then Z is every pixel coordinate in a similar “for loop” style row by row scan as the Mandelbrot).
That is seemingly how that functions.
I... understand??? Thank you!
how you are draw this function ?
Now I understand thank you
I find it easier to understand the process when you make the "negative root" part of the image appear stepwise
The "angular division" due to the square root makes the twists appear in the pattern.
The "radius contraction" due to the square root makes the conctraction of the patterns into the infinity small.
The "symetrical repetiton" due to the negative square root make the endless "production" of patterns.
And the c shift gives a specific "direction" in the process !
Because you started the reverse iteration from a complete circle of radius 2, and you arrived in a filled julia set,
does that mean that the orbits of the filled julia set will necessary go through any part of the circle ?
And it seems that the angular division from the square root operates on :
- the angle that go upward when the point is on the positive imaginary side
- the angle that go downward when the point is on the negative imaginary side
Why is that ?
Thanks fo your great vidéos by the way ! The animation are outstanding !
Technically yes
What is this application?
I wrote my own code in c++
You don’t need 4d things you can use 3d and the third dimension is iterations
Is the result the same if you change the initial shape ?
no, i wonder what that would be like tho
Can you do this for ANY image?
Yes. I have tried it actually.
@@TheMathemagiciansGuild can you make a video of you using many different images to form Julia Sets (or show me the link if you have made it already)?
Please let us now know what iterations switched over Julia’s? Let’s see:
10:21
8:09
8:11
8:13
More than a dozen iterations have Julia’s? Let’s see:
10:21
9:17
9:19
9:26
9:28
9:31
9:34
Maybe iterations go, this one will go away (always 20 months)
3:25
What? I only know division
1301
11:50
Therapist: Snake JUlia doesnt exist, it cant hurt you.
*Snake Julia:*