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

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

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

New bugfix release: https://mathr.co.uk/kf/kf.html#kf-2.15.2.3

- fix SIMD implementation of sgn() (test location by FractalAlex)
- fix opengl pack alignment for non-multiple-of-4 width bitmaps
- fix palette From Image not updating number of colours (reported by Microfractal)
- fix palette From Image to use maximum of width and height
- add PNG to supported images for palette From Image (reported by Microfractal)
- fix argmin|z| glitch correction for OpenCL
- report detailed timing information in command line mode
- update dependencies
- boost to 1.76.0
- tiff to 4.3.0
- openexr to 2.5.6
- glfw to 3.3.4

#KF #KF2 #KallesFraktaler #KallesFraktaler2 #Deep #Zoom #DeepZoom #EscapeTime #Fractal #Fractals #MandelbrotSet #BurningShip

kf-2.15.2 released with #OpenGL #GLSL colouring support (design your own colouring algorithms to post-process the calculated raw fractal iteration data)

Get it from https://mathr.co.uk/kf/kf.html#kf-2.15.2

#KF #KallesFraktaler #KallesFraktaler2 is #Fast #DeepZoom #FreeSoftware (#AGPL) for #EscapeTime #Fractal #Graphics (and #Video via additional programs like #zoomasm and others)

#x86_64 and #i686 builds are provided, it is technically possible to compile for #aarch64 but I couldn't get the resulting binary to work on my device. It's a #Windows #EXE that runs fine in #Wine on #Linux (where I do my coding). #armv7 builds seem to be blocked on what might be a bug in a third party library.

https://mathr.co.uk/kf/kf.html#kf-2.15.1.5
kf-2.15.1.5 released!

- fix long double rendering for hybrid formulas with abs
- fix typos breaking OpenCL floatexp bailout checks
- fix guessing for OpenCL floatexp
- fix endless reference loop in OpenCL
- merge changes from kf-2.14.10.6

https://mathr.co.uk/kf/kf.html#kf-2.14.10.6
kf-2.14.10.6 released!

- fix long double rendering for formulas with abs
- fix floatexp rendering for fractional bailout norm power
- fix some float conversion warnings and potential problems
- make prepare script modular (second argument determines libraries to build, default is all libraries)
- patch OpenEXR to try to fix issues with non-ASCII paths on Windows

#kf aka #KallesFraktaler #KallesFraktaler2 is #fast #DeepZoom #FreeSoftware for #EscapeTime #fractal like #MandelbrotSet #BurningShip etc. For Windows but works in Wine and is cross-compiled from Linux using MinGW.

#bird-eating #fish #fractal #art #fragmentarium #glsl #escapetime #hybrid

#colour #cycling #loop

```
fract(0.5 * dwell + time / 3.0) < 0.5
? vec3(1.0, 0.0, 0.0)
: vec3(1.0);
```

Where dwell (aka #continuous #escapetime) is computed 4x per pixel for image-space distance estimation (because using #gsls dFdx and dFdy on computed data is too low-resolution and fraught with peril in the event of incoherent control flow, works fine for the input smooth coordinates to know where to offset the 4x dwell computations).

For some reason I always seem to end up with #fractals that look a bit like insects

https://mathr.co.uk/et/i/ more #escapetime #fractals #monochrome #art