#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).

Deep inside

#fractalfriday #fractal #mandelbrot #escapetime #mathart

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

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

Added a section to the Fraktaler 3 page with links to some videos:

https://mathr.co.uk/web/fraktaler.html#Videos

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

Creamed Whip

https://diode.zone/videos/watch/89a4ca6a-197b-4ee5-9125-3c928273e8de

lockaccum (STROBE WARNING: 2m14s-2m36s, 5m16s-5m32s)

https://diode.zone/videos/watch/9e77e544-24e9-4fa9-924f-e9b3a144a889

rocks

https://diode.zone/videos/watch/79d82f2b-e8cd-4621-96ee-d2bc9cafce5c

Kalles Fraktaler 2 + development is mostly stopped from my side.

Here are some #AlternativeTo KF2+:

- FractalShades (Python)
- Fractal Zoomer (Java)
- Fraktaler 3 (C++)

For more details see:
https://mathr.co.uk/kf/kf.html#future

Important KF bug fixes may still be released from time to time, but I do not have enough time to implement the #BilinearApproximation (#BLA) optimisation in this project.

BLA is much better than #SeriesApproximation and #BivariateSeriesApproximation (which is called NanoMB1 in KF), in terms of efficiency of calculations, generality of applicability, simplicity of implementation, and robustness of results.

#KF #KF2 #KallesFraktaler #KallesFraktaler2 #Kalles #Fraktaler #fast #deep #zoom #DeepZoom #EscapeTime #fractal #Mandelbrot #MandelbrotSet #BurningShip

Rainstorm

https://diode.zone/videos/watch/babc15b0-0123-48d9-aa69-e6cd3ec940ed

Zhuoran's "reset reference count" trick for avoiding #glitches in #perturbation rendering of #EscapeTime #fractals also works for #hybrids.

For a hybrid of 4 formulas in a loop, you need 4 references, one for each starting phase, because the reference count can be reset at any iteration, not just the start of the loop. In general you need preperiod+period many, and even more (and the logic gets more complicated) if they have more than one critical point... I've not done that yet.

Each of those references (which can be computed in parallel) can have a bilinear approximation acceleration structure applied to skip multiple iterations in one step (where the non-linearity is tiny). These can also be computed in parallel (though they can be parallelized individually too, doing it in bigger chunks should be more efficient).

Overall this makes the overall process a lot faster than the old "detect glitches and correct them later with another reference, repeat" process. For the attached image, BLA acceleration gave a 46x speedup (in terms of number of steps performed) over doing plain perturbation iterations.

Ref: https://fractalforums.org/fractal-mathematics-and-new-theories/28/another-solution-to-perturbation-glitches/4360/msg29835#msg29835

kf-2.15.5 released!

full announce: https://mathr.co.uk/blog/2021-12-05_kf-2.15.5_released.html

highlights include single reference implementation for glitch avoidance (as suggested by Zhuoran on fractal forums), and lots of new formulas (mostly from FractalAlex)

this is probably the last kf release from me for the foreseeable future...

#KF #KF2 #KallesFraktaler #KallesFraktaler2 #fractal #fractals #MandelbrotSet #BurningShip #EscapeTime #DeepZoom

Separated Perpendicular

https://diode.zone/videos/watch/de5c8192-ec23-4a19-a6ce-c19acee66aa3

Separated Perpendicular (feat. glitches)

https://diode.zone/videos/watch/cc85a810-818c-4eb9-bfa7-ef7d0a8a401a