[Visual] Modular Form - Level 1 Weight 12 (Ramanujan Delta Function)

[@scrattyrat]

Incredible visualisations! I can't begin to think how you programmed that in blender based off the maths, I have been trying to visualise modular forms in Touchdesigner and its extremely challenging. Very impressive stuff 👍

[@michaelzumpano7318]

This was beautiful. I’d love to see a deep zoom on the top bifurcation zones. Modular forms are mind blowing.

[@MMW1531]

Super meticulous form, really amazing.

[@ARBB1]

Great work on this series mate.

[@dmit10]

Thanks for that! Waiting for Gamma function

[@Mortiis558]

This totally didn’t go over my head!

[@brian8507]

These are graphs of complex functions ... a special class of them where they repeat the entire bebehavior in tiles that tile the plane. Weird crazy number lore comes from these functions... prime number lore for example... and connections to other unrelated areas of deep math... like the monster group. It's nuts bro

[@bini420]

@@brian8507 interesting. What determines the color and height? I thought the complex plans was 2d also I thought modular forms were some sort of operation like addition and subtraction, what I are they

[@brian8507]

@bini420 so to graph a complex function... you would need 4 dimensions. So to get around this that encode color and brightness to the output values. Color representing the argument (or angle) of the complex number and brightness being the magnitude of the output. So pure white would be infinity and black is a zero. And red could represent a positive real... cyan being a negative real... and all the colors in between being different complex numbers that exist on the unit circle. Lol It's better if I have a blackboard sorry

[@Mortiis558]

@@brian8507 I missed your original reply until now, but thanks for the explanation. You have any good sources for “number lore” ?? I get what you mean by it, so basically I am asking if you know any good sources for higher level math or general math?

[@brian8507]

@@Mortiis558 let me know if u got that

[@Darrida]

One should know that modular forms graphic is a simplification. The real graphic is in fourth dimension. Si no human being can visualize what it looks like.

[@BenNBuilds]

I love your work!

[@stanervin6108]

Interesting form.

[@yoavmal]

Down in each, what happens? Is it undefined? Is it behaving the same but mirrored to the negatives?

[@BuleriaChk]

Proof of Fermat's Last Theorem for Village Idiots (works for the case of n=2 as well) To show: c^n a^n + b^n for all natural numbers, a,b,c,n, n >1 c = a + b c^n = (a + b)^n = [a^n + b^n] + f(a,b,n) Binomial Expansion c^n = [a^n + b^n] iff f(a,b,n) = 0 f(a,b,n) 0 c^n [a^n + b^n] QED n=2 "rectangular coordinates" c^2 = a^2 + b^2 + 2ab Note that 2ab = 4[(1/2)ab] represents the areas of four right triangles) "radial coordinates" Lete p:= pi, n= 2 multiply by pi pc^2 = pa^2 + pb^2 + p2ab Note that pc^2, pa^2, and pb^2 represent areas of circles, wile p2ab = a(2pb) is the product of a radius (a) and a circumference (2pb). This proof also works for multi-nomial functions. Note: every number is prime relative to its own base: a = a(a/a) = a(1_a) a + a = 2a (Godbach's Conjecture (now Theorem...., proved by me :) (Wiles' proof) used modular functions defined on the upper half of the complex plane. Trying to equate the two models is trying to square the circle. c = a + ib c* - a - ib cc* = a^2 + b^2 #^2 But #^2 = [cc*] +[2ab] = [a^2 + b^2] + [2ab] so complex numbers are irrelevant. Note: there are no positive numbers: - c = a-b, b>a iff b-c = a, a + 0 = a, a-a=0, a+a =2a Every number is prime relative to its own base: n = n(n/n), n + n = 2n (Goldbach) 1^2 1 (Russell's Paradox) In particular the group operation of multiplication requires the existence of both elements as a precondition, meaning there is no such multiplication as a group operation) (Clifford Algebras are much ado about nothing) Remember, you read it here first) There is much more to this story, but I don't have the spacetime to write it here. see pdfs at physicsdiscussionforum dot org

[@monoman4083]

nice...

[@joakimswahn9179]

This looks like a fractal.

[@matthewkemp5343]

Haha, the complexity of the modular form messes with KZbin's playback/compression algorithm. If you skip around the video the colors will have their hue's shifted for a split second.

[@SmokeyDope]

looks like a branching/biforcating tree fractal

[@TheMathemagiciansGuild]

Yes, you are correct. Modular forms are branching fractals as they approach the real number line.

[@guill3978]

Aa fractal

[@gametalk3149]

This looks beautiful, but the synthetic pads are stabbing my ears