Throwback to last year: My Mandelbrot Wellerman

ASCII pirate by @ngons

#parody #wellerman #mandelbrot #burningship #fractal #codeart #mastoart

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

Worked a bit on #CommonSubexpressionElimination #CSE today. Saving one addition in the perturbation inner loop makes #BurningShip take 6% less CPU time in that phase. Doing some more for the derivatives saves 17% overall. Other formulas show higher savings, but it's slow doing these by hand (KF has around 100 formulas, today I optimized 5 of them...).

https://code.mathr.co.uk/kalles-fraktaler-2/blobdiff/997b1df0f9d05b8dc0a5da598153fcf6e0ee3f39..45fb14996da61c118e96270e9f7edccb6b769435:/formula/formula_1_2.xml

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

https://mathr.co.uk/kf/kf.html#kf-2.15.1.6
https://mathr.co.uk/kf/kf.html#kf-2.14.10.7

Two bugfix releases of #KF in current branch and stable branch: turns out switching #MinGW from #Win32 to #POSIX #threading model had some unforeseen consequences (aka bugs, one of which was "zooming out sometimes resets zoom to infinity or zero" which broke interactive use), so I reverted those changes.

#KallesFraktaler2 is fast #fractal #DeepZoom #FreeSoftware for #MandelbrotSet #BurningShip etc

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.

kf-2.15.1 released!
with OpenCL acceleration, hybrid formula designer, exponential map, and more
get it from https://mathr.co.uk/kf/kf.html#kf-2.15.1

- #OpenCL support for perturbation iterations (requires double precision support on device: #CPU should work, some #GPU might not)
- #HybridFormula editor (design your own fractal formula)
- #ExponentialMap coordinate transformation (useful for export to #zoomasm for efficient #video assembly)
- rotation and skew transformations are rewritten to be more flexible (but old skewed/rotated KFR locations will not load correctly)
- kf-tile.exe tool supports the new rotation and skew transformations
- the bitrotten skew animation feature is removed
- a few speed changes in built in formulas (one example, RedShiftRider 4 with derivatives is almost 2x faster due to using complex analytic derivatives instead of 2x2 Jacobian matrix derivatives)
- flip imaginary part of Buffalo power 2 (to match other powers; derivative was flipped already)
- slope implementation rewritten (appearance is different but it is now independent of zoom level and iteration count)
- smooth (log) iteration count is offset so dwell bands match up with the phase channel

#deep #zoom #DeepZoom #fractal #fractals #free #software #FreeSoftware #mandelbrot #MandelbrotSet #BurningShip #KallesFraktaler #KF

"Charred Bard"

https://archive.org/details/charred-bard
https://youtu.be/NMKBBk-yf_4

#Zoom into a #hybrid #fractal, in black on white with rainbow fringes.

59 iterations of #MandelbrotSet formula, then 1 iteration of #BurningShip formula, then repeat, until escape.

137bpm #techno soundtrack is composed in #Clive, using tempo-synced feedback delays with 1/2-octave bandpass filter bank, where each band's gain depends on the level of the bands below.

Rendered as an exponential map with work-in-progress KF-next, using a custom zoom assembler to flatten it into video frames.

https://archive.org/details/special-branch

Short #zoom into a #hybrid #fractal, in black on white with rainbow fringes.

59 iterations of #MandelbrotSet formula, then 1 iteration of #BurningShip formula, then repeat, until escape.

Soundtrack is an experiment in extreme timestretching.

Rendered as an exponential map with work-in-progress KF-next, using a custom zoom assembler to flatten it into video frames.

kf-2.14.10.2 released
https://mathr.co.uk/kf/kf.html#kf-2.14.10.2

- store zoom out sequence was saving JPEG contents in PNG filenames sometimes
- store zoom out sequence was forcing some kind of center reuse even when not requested (reported by saka and Azula)
- store zoom out sequence was sometimes not saving metadata in image files correctly
- setting bad SIMD vector size in KFS could crash (reported by FractalAlex)
- setting window size/image size from KFS should be better behaved now
- refactor default loading (now it loads default location kf.kfr from next to EXE, as well as default settings kf.kfs; defaults are only loaded when respective command line options are not given)
- don't recalculate fractal when changing window size (reported by FK68)
- fix buffer overflow crash in iterdiv -> string for GUI, also fix loss of precision (reported by FK68)
- fix typos causing last few pixels to be corrupt in SIMD
- remove annoying dialogs about derivatives (requested by gerrit)

- upgrade to boost 1.73.0
- upgrade to mpfr 4.1.0
- upgrade to tiff 4.1.0
- upgrade to glm 0.9.9.8
- upgrade to openexr 2.4.2

- don't upgrade to pixman 0.40.0 ( https://gitlab.freedesktop.org/pixman/pixman/-/issues/43 )

#fractal #mandelbrot #BurningShip #deep #zoom #BugFix

KF 2.14.10 released! Highlights:
https://mathr.co.uk/blog/2020-05-25_kf_2.14.10_released.html

#KallesFraktaler2 #KF #Fractal #Mandelbrot #BurningShip etc #DeepZoom #Software #Perturbation #SeriesApproximation

Big changelog this time: read it and download from https://mathr.co.uk/kf/kf.html#kf-2.14.10
(binaries for 64bit Windows run in Wine on Linux where I do my coding, cross-compiling using #MINGW64)

new #kf #release https://mathr.co.uk/kf/kf.html#kf-2.14.8

- feature: SIMD support for accelerated perturbation calculations at shallow-to-moderate zoom depths.
- feature: Newton-Raphson zooming completion estimate (number of steps)
- feature: Newton-Raphson zooming progress backups (after each step)
- feature: fewer required fields when loading location parameters (allows loading the NR-zoom backups)
- feature: directional DE stored in EXR as `DEX` and `DEY` channels, and used for slopes colouring with `Analytic` differences (requires derivatives, fixes noisy texture when jitter is enabled)
- feature: 64bit iteration count support (limit is now 9 exa-iterations up from 2 giga-iterations), use EXR for export. This feature is very experimental, I haven't had the patience to test it properly. Please report back success or failure.
- note: periods are still 32bit and limited to 2 giga-iterations
- bugfix: command line --save-exr now sets non-interactive mode flag.
- note: built for 64bit only; 32bit hardware is obsolete by now.
- note: distribution package compressed with 7-zip for smaller size.
- upgrade to openexr 2.4.0
- upgrade to mingw64 g++ 9.2.1-8+22~exp1 (Debian experimental) and rebuild everything

#mandelbrot #BurningShip #fractals #deep #zoom

Trying to get "scaled double" #maths working for #BurningShip #fractal in #kf. Purpose of rescaling is to avoid floating point underflow to 0.0. Something is broken however, I suspect it has to do with glitch detection as dead-center miniships do much better).

Burning Ship iterations:
Xrn = Xr * Xr - Xi * Xi + Cr;
Xin = abs(2 * Xr * Xi) + Ci;

Perturbed Burning Ship iterations:
xrn = (2 * Xr + xr) * xr - (2 * Xi + xi) * xi + cr;
xin = 2 * diffabs(Xr * Xi, Xr * xi + xr * Xi + xr * xi) + ci;

Rescaled perturbed Burning Ship iterations (S * s = 1, actual orbit is X + x * s):
xrn = (2 * Xr + xr * s) * xr - (2 * Xi + xi * s) * xi + cr;
xin = 2 * diffabs(Xr * Xi * S, Xr * xi + xr * Xi + xi * xr * s) + ci;

diffabs(Z,z) evaluates abs(Z+z)-abs(Z) without catastrophic precision loss, by doing case analysis on the signs of Z and Z+z. Technique invented by laser blaster at fractalforums.com.

#Mandelbrot / #BurningShip / Mandelbrot #hybrid #fractal #art

Parameter data for #et (usually this is stored in image metadata, but Mastodon strips that out...):

```
MBM
z := z^p + c
z := (|x| + i |y|)^p + c
z := z^p + c

p=2
q=1
d=1.0
e=0.0
a=-0.19713518046622788536003
b=-0.65184481359655471603044
r=1.9073486328125e-6
t=(8.715574274765861e-2,0.9961946980917454,-0.9961946980917454,8.715574274765861e-2)
n=4096

de=1.0
```

I got #interior checking working for the #BurningShip , based on Xavier Buff's method for the Mandelbrot set presented by Arnaud Cheritat: https://www.math.univ-toulouse.fr/~cheritat/wiki-draw/index.php/Mandelbrot_set#The_idea

Replace `der` by the Jacobian $L$ w.r.t. $(x_1, y_1)$. Replace `squared_modulus(der)` with $|\det{L}|$. Arbitrarily use the pixel spacing for `eps`.

Should be straightforward to generalize the idea for other formulas.

The red zone of unknown is troubling - I wonder what is really going on in there.

#hybrid #Mandelbrot #BurningShip #fractals #monochrome #art #bubbles

a = 0.1343601340757372719363390615284261744165
b = -0.6851921014889349327518356825806140975126
s = 7.3485744548807846e-24
t = (1,0,0,1)
formula:
z := z^2 + c
z := z^2 + c
z := (|x| + i |y|)^2 + c
z := (|x| + i |y|)^2 + c

#quartic (power 4) #BurningShip #fractals #art #monochrome #opart

a = 0.639842372544549201204928357495775021977648268509402840359034
b = 0.135996460127830318428355021688587977964732034634690759751358
s = 5.7332335426957978e-43
t = (0.6928120449739648,-0.713231167787216,0.7163656381606373,0.7059139674028518)

#BurningShip #fractals #art #monochrome #lines

```
a = -1.7641372147884787988956820414441815
b = -3.1027166627556593979334487138566918e-2
s = 8.6736173798840355e-19
t = (0.6692182114898958,3.0642424452739516,2.90512202528787,14.796366937687294)
```
(`a+bi` is coordinates of center, `s` is inradius of view, `t` is a site-specific non-uniform stretch 2x2 matrix transformation applied to the pixel coordinates)