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bamia
I started building my website where I share some of my work, and this is my first article.

I explain in detail how an image can be inserted in a Mandelbrot/Julia set.

Again, sorry for my English.

namanyayg
Some great results, both mathematically and visually. Learnt a bunch. Thanks for putting it up online!
namanyayg
Anyone else seeing a rotating snakes-esque illusion in the first few fractals?
Rexxar
Switching between this and a blank page make it incredibly visible for me.
gedy
I did some work on this in JavaScript a while back: http://garythom.as/myo/julia/

(Images are not uploaded, all in browser)

bamia
Nice! How did you discover this method? How did it all began?
gedy
A friend of mine found on his own about 20 years ago programming fractals in Amiga basic, and since then have I ported/played with to Java, C++, and eventually JavaScript.

Here's the results of an AfterEffects video plugin I wrote about 2003: https://vimeo.com/105310176

Rexxar
You should do a "Show HN" for it. I think a lot of people will like it.
n3k5
> Maybe one day I will revisit this project and properly rewrite the whole thing.

I recommend doing it in GLSL. It's very little effort to implement (about 30–50 lines of code) and even on a modest GPU it'll run fast enough so you can explore different parameters interactively. As a bonus, you can get MIP-mapping for basically free — no more aliasing!

In case you don't want to learn OpenGL or Vulkan, you can use a tool such as Shadertoy.

DerDangDerDang
Writing fractal shaders is great fun, agreed. I found mip mapping introduced artefacts around discontinuities in the texture coordinates - this was doing orbit trap texturing, but the UVs in the described method would have similar discontinuities. The artefacts can be reduced with a bit of care, iirc
eroeroe
Yes, I agree: the GLSL is a adding value.

I found great and fabulous this: https://www.michelemorrone.eu/glchaosp/

glChAoS.P ⋅ wglchaosp.p - Real time 3D strange attractors GPU explorer... and hypercomplex fractals

It's both OpenGL and WebGL (via WebAssembly), also opensource and multi platform.. and explores over 100 types between attractors, fractals and also DLA3D (Diffusion Limited Aggregation)

Very beautiful!