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#mandelbrot

3 posts3 participants0 posts today
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Amand Tihon

Hey mastodon, j'aimerais beaucoup retrouver les listings #QBASIC qui avaient été publiés dans les #ScienceEtVieJunior de mon adolescence (encore mieux si c'est avec les articles associés).

Je me souviens plus particulièrement d'un visualiseur #Mandelbrot / #Julia, d'un #Tetris et d'un générateur d'#autostéréogramme

Je ne les trouve ni sur #archiveorg ni sur d'autres sites moins recommandables. Est-ce que quelqu'un aurait ça ?

Boosts appréciés.

#retrocomputing#basic
Microfractal

#FractalFriday (It's already Saturday)

Elephant valley of the Mobius Mandelbrot set.

Formula: \(z_{n+1}=f(z_n^2+c,1)\)

where \(f(z, a)\) is defined as (C-like pseudocode):

Complex f(Complex z, Real a) {
Real dist = abs(re(z)) - a;
if (re(z) > a) {
re(z) = -a + dist;
im(z) = -im(z);
} else if (re(z) < -a) {
re(z) = a - dist;
im(z) = -im(z);
}
return z;
}

Coloring is done by using three very similar colormaps, mapped to triangle inequality average values.
The final color is produced by interpolating between these three colors using the so called "atom domains".

Generated using my GLSL Shadertoy fractal generator: shadertoy.com/view/33sSRf

#Mandelbrot#Fractal#Art
Oscar Cunningham

I made a Mandelbrot & Julia set explorer! codepen.io/Oscar_Cunningham/fu

I was watching @standupmaths's video youtube.com/watch?v=0OP9guFmWf about Mandelbrot and Julia sets, and I could see he was clicking around in @christianp's app looking at the Julia set corresponding to each point in the Mandelbrot set. But I wanted to also be able to click around in the Julia set and see how the Mandelbrot set changed.

Really both the Mandelbrot and Julia sets are two dimensional cross sections of a four dimensional fractal. A point (x,y,a,b) is in this set if the function z ↦ z²+(x+yi) doesn't diverge when iterated starting at a+bi. My app lets you see the slices of (x,y) for fixed a and b, and also (a,b) for fixed x and y.

I don't write JavaScript, so all code is bad and/or stolen.

#Math#Maths#Mathematics
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Microfractal

#Fractalfriday
I updated my #Shadertoy #fractal explorer. Link: shadertoy.com/view/33sSRf
It now supports skewing the C-plane using a quad of four draggable points. The coefficients 'a' and 'b' can now also changed by the mouse. To show the points, simply hold the space bar.

Here is a video which demonstrates that.
The formula is \(z_{n+1}=z_n^2*\frac{z_n-a}{z_n-b}+c\)
where a and b are the blue points in the video.

#Mathart#GLSL#Mandelbrot
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