zoomasm assembles zoom videos from exponential map key frames, as exported by #Fraktaler #Fraktaler3 and other software for
#DeepZoom #fractals #MathArt
Changes in version 3.4 (2025-06-11) since version 3.3 (2023-07-13):
- support dual channel iteration counts (N0+N1) for very high iteration counts (above 4 giga iterations)
- update to current library versions
binaries for Windows, built from Debian Linux, source for all those platforms. new homepage at
#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).
#fraktaler #fraktaler3 v3 final is still not released after almost a year... trying to squash final #bugs in the coming weeks, so now would be a good time to check the #beta to find problems, so I can #fix them...
known bugs that have been fixed already but not yet released include:
- negate Y option has bad reference leading to glitches / fantasy fractals
- floatexp opencl coordinate glitch (looks like horizontal stripes of the image repeated vertically) with deep zooms on GPU
- newton zoom dialog has been improved
- some other small things
links to beta downloads for Windows (EXE), Android (APK), Linux (compile from source), Web (try in browser) via https://mathr.co.uk/web/fraktaler.html#Version-3-Beta
inspired by tavis' deep field #nebulabrot #DeepZoom images on #fractal #fractals forums, I did a little shader that for each c in the complement of the #MandelbrotSet M, colours according to how often z <- z^2 + c hits a given small target disc , weighted by derivative (as a proxy for point density).
it looks as though the hit sources are distributed everywhere near the boundary of M, which i think i can prove for target discs outside a sufficiently large esape circle, but i'm not sure how for discs nearer M. intuitively, by the time any cell pair in binary decomposition of exterior escapes, it covers an annulus with radii R, R^2, so any disc outside R will be hit by some region in every cell pair.
A recursive journey
..into the Mandelbrot set.
Coordinates:
x: -1.749920829766361615957924535067052355476842068687777470902374182113643194199531115425932939351952998444521471782733345
y: -0.000008314197505662832868240412422750221195897400965310578374103549328243894493064964400167347770028467256855870798659751015
size: 2.8574684782056875E-96
#fractal #mandelbrot #mathart #deepzoom #mandala #digitalart
Finally got the linear approximation algorithm, which is based on perturbation theory to work in my fractal generator.
It speeds up the image computation by skipping a lot of iterations based on some precomputed coefficients.
The coordinates of the displayed fractal can be found here: https://ff1.fractalforums.org/index.php?topic=17263
without this algorithm, the computation would take hours instead of a minute.
#mandelbrot #fractal #perturbation #linearapproximation #deepzoom
Got perturbation to work for Julia sets.
This is a Mandelbrot-Julia set for the point at
x: -0.104265130874779131079794344471474183643970478275392768565796119633
y: 0.649570728986384674344306272154528337425865744687331575800591618967
for comparison, I attached a second image showing that point in the Mandelbrot set.
Millionaires 001 (The Making Of)
https://diode.zone/videos/watch/0ddeed9b-6cfd-4fe6-a85e-0342b95b6284
Think I forgot to announce this here (oops): I have a new paper about artist-constructed patterns in Mandelbrot set zooms
https://mathr.co.uk/web/m-patterns.html
> Heiland-Allen, Claude. 2023. “Patterns in Deep Mandelbrot Zooms.” In Algorithmic Pattern Salon. Then Try This. https://alpaca.pubpub.org/pub/uqh84mma .
> The Mandelbrot set emerges from iterations of z→z^2+c. Zooming deep into the fractal, history repeats each time the navigator veers off-centre, doubled up and twice as fast. At each resulting crisis, decisions allow patterns to be sculpted in the intricate shape of the boundary. Patterns in the decisions made when zooming are reflected in the complex dynamics, in particular in the binary expansions of the pairs of external rays landing on the cusp of each baby Mandelbrot set copy at the centre of each phase. Numerical and symbolic algorithms are used to analyze the pattern of decisions given the final coordinates of artworks by several fractal artists. New families of patterns can be synthesized, and from them coordinates can be calculated for image generation. In this way the manual labour of constructing deep Mandelbrot zooms can be reduced, allowing more time for pattern design.
Streaming from 14:00 UTC today (just over 3.5 hours from now), link at
https://salon.algorithmicpattern.org/schedule/
(will be recorded)
Started a new series of #Mandelbrot #DeepZoom #fractal #art pieces.
Concept: stop zooming once the period of the central baby Mandelbrot set exceeds one million.
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
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
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
https://mathr.co.uk/blog/2021-06-04_old_wood_dish.html I wrote a blog post with analysis and variations on a theme by jwm-art from 2010
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
New blog post "deep zoom theory and practice"
https://mathr.co.uk/blog/2021-05-14_deep_zoom_theory_and_practice.html
#deep #zoom #DeepZoom #fractal #fractals #mandelbrot #MandelbrotSet #BurningShip #graphics #math #maths #mathematics #FloatingPoint
What to do about the Examine Zoom Sequence feature of #KF #KF2 #KallesFraktaler #KallesFraktaler2 (a #Deep #Zoom #DeepZoom #Fractal #Fractals explorer)?
It's probably no longer necessary now that Reuse Reference (which saves computation time at the expense of memory) can be used together with Auto Solve Glitches (which is needed for correct images)?
It used to be (in the distant past) that zoom out sequences were full of glitches and you'd have to scroll through and correct them later, but the code rotted and there are loads of bugs (it doesn't support iteration data in EXR, only KFB, it doesn't write out corrected PNGs etc, only JPEGs, minimizing the window can corrupt the whole zoom sequence, ...).
There is also a poll here:
https://fractalforums.org/kalles-fraktaler/15/examine-zoom-sequence-poll/4206/msg28491#msg28491
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.
