#Fraktaler #Fraktaler3 v3.1 #release

#DeepZoom #hybrid #EscapeTime #fractals #MathArt #MandelbrotSet #BurningShip

binaries for Web, Android and Windows, built from Debian Linux, source for all those platforms

https://fraktaler.mathr.co.uk/

changes since v3 (June 2025):

- histogram colouring

- partial KFR importer (no colouring yet)

- web version uses full window canvas

- doubleexp number type

- float128 number type (where available)

- fix: correct matching between appearance of CPU and OpenCL backends (thanks to JWM for reporting)

- fix: compatibility with toml11 v4.

- fix: builds and runs in Termux + Termux X11 on Android

- fix: no 'quit when done' option on Web or Android.

- fix: correct status when pressing ESC after rendering is complete.

- internal: build system improvements.

wavy iteration bands that just touch each other, for hybrid quadratic Julia set where the c value varies during iteration (e.g. looping several values).

calculation inner loop snippet:

```
vec2 C1 = C;
C = c[iteration % count];
vec2 origin = C1 + vec2(100.0, 0.0);
float o = length(origin);
float e = (1.0 + 2.0 * o) / 2.0;
float r = sqrt(e * e - o * o + o) + e;
if (length(z - origin) > r) break; // escaped
z = cSqr(z) + C;
```

#JuliaSet #hybrid #EscapeTime #fractals #MathArt #CreativeCoding #GLSL #ComplexDynamics #maths

don't ask me how I derived r, I forgot to save my workings from a couple of years ago

tune 100+0i to taste (may break when small)

#Fraktaler #Fraktaler3 v3 #release

#DeepZoom #hybrid #EscapeTime #fractals #MathArt

binaries for Web, Android and Windows, built from Debian Linux, source for all those platforms

https://fraktaler.mathr.co.uk/

changes since v2.1 (July 2023) are too many for this toot, the main new feature is flexibile colouring with GLSL shader fragment.

changes since v3~preview (June 2024) are quite small (a few bug fixes, some enhancements).

Asymptotic circular

Formula:
\(z_{n+1} = z_n^2\frac{|re(z_n)|+|im(z_n) |*i}{z+a}+c\)
with \(a = 0.25\)

Coordinates:
x: -0.10234600611335453882872
y: -0.14437536422400950518792
size: 6e-07
#fractal #fractalart #mathart #digitalart #escapetime

Here is the output: a fast zoom into the fractal (~ to 1e-85).

#escapetime #mandelbrot #fractal #zoom #animation

Perturbation for

\( z_{n+1} = (|re(z_n)| + i*|im(z_n)|)^2 e^\frac{0.01}{z_n+c}+c \)

#burningship #fractal #escapetime #animation

Added perturbation for \( e^z \) into my program. Unfortunately, there seem to be some glitches that are resistant to rebasing.

Nevertheless, a zoom-in animation into \( z_{n+1} = z_n^2 e^{\frac{0.0001}{z_n+c}}+c \)

#fractal #mandelbrot #exponential #animation #escapetime

Fraktaler-3 version 1.2 released!

This is a bugfix release in the 1.x series, fixing some small issues.

Most users should probably wait for the 2.1 bugfix release in the 2.x series, coming soon.

Documentation:

https://fraktaler.mathr.co.uk/fraktaler-3-1.2.html

Download (source code, Windows EXEs, Android APK, manual PDF):

https://fraktaler.mathr.co.uk/download/1.2/

Live version (runs in your web browser):

https://fraktaler.mathr.co.uk/live/1.2/ (but it turns out it is broken, will see if I can fix it soon..)

#Fraktaler #fast #deep #zoom #DeepZoom #hybrid #EscapeTime #fractals

https://fraktaler.mathr.co.uk/ version 2 released

fraktaler 3 is a fast deep zoomer for hybrid escape time fractals

version 2 brings a new opcode-based formula engine (faster computationally, more robust mathematically, more flexible artistically) and wisdom configuration GUI (no more running obscure commands and editing configuration text files).

try it live in your browser

binaries for windows and android

source code under GNU AGPL3 tested on Debian

#fast #deep #zoom #DeepZoom #hybrid #escape #time #EscapeTime #fractal #fractals