Mastodawn

#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

#MandelbrotSet #BurningShip #fractals #MathArt #DeepZoom

Fraktaler 3 :: mathr

A fast cross-platform deep zoomer for hybrid escape time fractals.

Microfractal 🫖Apr 18, 2025

Decagon (fractal version)

\(z_{n+1}=fold(z_n)^2+c\)

where fold is a generalized absolute value function. A complex number has two components: a real and an imaginary part.
If we take the absolute value of one of these parts, we can interpret this as a fold in the complex plane. For example, |re(z)| causes a fold of the complex plane around the imaginary axis, which means that the left half ends up on the right half. If we do this for the imaginary component |im(z)|, we fold the complex plane around the real axis which means that the bottom half ends up on the top half.
These two operations are quite similar, because the imaginary fold is just like the real fold of the plane, except that it was previously rotated 90 degrees (z * i). But what if we rotate the plane by an arbitrary number of degrees?
An arbitrary rotation of the complex plane can be expressed as rot(z, radians) = z * (cos(radians) + sin(radians) * i), where radians encodes the rotation.

The image here is produced, by rotating the plane exactly five times, and folding the imaginary part each time.

I found this algorithm in the Fractal Formus under the name “Correction for the Infinite Burning Ship Fractal Algorithm”.
It can be seen as a generalization of the burning ship obtained by folding the complex plane twice with a rotation of 90 degrees, i.e. folding both the real and the imaginary part.

#fractalfriday #fractal #burningship #mandelbrot #complexplane #complexnumbers #mathart #math #escapetimefractals