Re: The splendor of true

Le 11/03/2025 à 00:19, Python a écrit :

Le 11/03/2025 à 00:09, Richard Hachel a écrit :

Le 10/03/2025 à 22:21, "Chris M. Thomasson" a écrit :

On 3/8/2025 3:54 PM, Richard Hachel wrote:

>
>
<http://nemoweb.net/jntp?gpYr5eUNsnuIlHzO4tsg1kWypUg@jntp/Data.Media:1>
>
What is this?
>
R.H.

>
In C (complex numbers as defined in math i.e. R[X]/(X^2 + 1)) consider the sequence :
(z_n and c are complex numbers)
>
z_0 = 0 + 0i
z_(n+1) = (z_n)^2 + c
>
if (z_(n)) does not go to infinity then c is a member of Mandelbrot's set
(it is also the set of c for which another set (Julia's set J_c) is connexe)
>
You can explore it there on line (zoom on the border, it is quite fascinating) :
>
https://mandel.gart.nz/
>
There the set itself is the black part, the colors at the border represents how fast the sequence diverges.

 Note that the small "copies" of the whole set you would notice look not quite right at high zoom, this is because of limited (fixed) precision of floating point numbers in JavaScript.

I implemented this on a SUN Workstation in C on SunView Desktop Environment (no X11) for UNIX SunOS, as a student, back in 1992 using variable (arbitrary) precision floating point numbers (long floats).
Computing was slow back then but small copies of the set looked exactly as the whole set even at high zoom.