How to Build a Julia Set

[@DrakenFire]

Fascinating. After seeing your videos i understand why mathematicians often say that math is art.

[@lagduck2209]

Sir this is pure gold, I feel lucky to be among 5325 lucky viewers of your art

[@lagduck2209]

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..

[@TheMathemagiciansGuild]

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.

[@lengeschder]

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!

[@live22morrow]

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.

[@ricardasist]

Amazing! This is a gem channel!

[@TheMathemagiciansGuild]

Thank-you. I appreciate the kind words.

[@beanos5105]

best video of julia set explanation on youtube! thanks man, you reallu made my life easier. instant like

[@ilikepizza9889]

I was so surprised you only have 900 subscribers, this video is awesome keep it up!

[@clarkowen4661]

Whoa I didn’t even notice lol! This page is on the edge of blowing up probably

[@flixgribv]

Thank you for this video, it made it kinda easier to understand how does this actually work!

[@TheGandorX]

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.

[@theothersidenumber9307]

Your still dummy ing it lol.

[@denelson83]

You should have also done a Julia set for a Misiurewicz point, such as c = I.

[@Intrebute]

Does the example that ends at 14:16 ever break apart? It feels like it's always closer and closer to exploding into dust

[@TheMathemagiciansGuild]

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).

[@elizabethojinal4228]

@Tagliaferri Andrea program i think????

[@THE_ONLY_GOD]

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.

[@elizabethojinal4228]

My favorite Julia set is the last part. And the disconectted Julia is called the Fauto Dust

[@YourPrerogative]

Fantastically helpful

[@cacamikaz71]

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 ?

[@cacamikaz71]

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 !

[@pannkakan1986]

Technically yes

[@cacamikaz71]

I find it easier to understand the process when you make the "negative root" part of the image appear stepwise

[@cacamikaz71]

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 !

[@wallywutsizface6346]

I... understand??? Thank you!

[@MaxKili2177]

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!

[@ishu4227]

11:50 Therapist: Snake JUlia doesnt exist, it cant hurt you. *Snake Julia:*

[@hamzahamxa5951]

how you are draw this function ?

[@cacamikaz71]

Is the result the same if you change the initial shape ?

[@vindi167]

no, i wonder what that would be like tho

[@bachirblackers7299]

Great job

[@zfloyd1627]

Can you do this for ANY image?

[@TheMathemagiciansGuild]

Yes. I have tried it actually.

[@zfloyd1627]

@@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)?

[@arado240dd]

What is this application?

[@TheMathemagiciansGuild]

I wrote my own code in c++

[@Blue-hs9tv]

Now I understand thank you

[@Idkgivemeone]

You don’t need 4d things you can use 3d and the third dimension is iterations

[@magnoliamcginley6972]

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)

[@TheInfinityPower12354]

3:25

[@Adam46221]

What? I only know division

[@Mr.Belemore]

1301

[@ishu4227]

11:50 Therapist: Snake JUlia doesnt exist, it cant hurt you. *Snake Julia:*