what's the the best path[road] to learn shaders and fractals

I Have Many problem with find any resource to learn shader i can't find any resource to this field of science i learned c/c++ java, python .... also learn Basics of OpenGL on Intermediate mode and core mode some shader basic

but till confused with [shaders and fractals] i think this filed very relative to mathematics no problem i study many levels of maths in my college

but i need to the path what's the path to learn make thing like this 3D Fractal Animation:

But Please don't advice me to learn Mandelbulb 3D because it's just a tool

i need to learn the core of this filed of science [like a sahdertoy site shader programmers] then i will learn how to use Mandelbulb 3D but now i need to learn shader

and why there is no book or course learn those things?

another question

look at this video 11 Dimensions - Mandelbrot Fractal Zoom (4k 60fps)

What's meaning of 11 Dimensions : is it a infinite Dimensional equation[Stochastic Equations in Infinite Dimensions]?

[I Apologies if there is some mistakes : english isn't my native language]

Solution

It's a pretty long and winding road learning how to draw fractals. The math books don't teach you how to program them and the programming books don't teach you the math.

Start with a Mandelbrot 2D. It's not too difficult, you're going to need to know or learn:

complex numbers (what they are, how to add and multiply)
converting between coordinate systems (complex plane -> on screen canvas)
color palettes and how to pick a nice one that shows the features of the set

Here's a good tutorial on how to make a Mandelbrot 2D generator. Play around with it and you'll probably be able to ask some more specific questions.

I bought this book a while ago, Chaos and Fractals: New Frontiers of Science, it's a big one! I haven't read more than a few chapters, but it might be more what you're after.