#Fractalfriday
I updated my #Shadertoy #fractal explorer. Link: https://www.shadertoy.com/view/33sSRf
It now supports skewing the C-plane using a quad of four draggable points. The coefficients 'a' and 'b' can now also changed by the mouse. To show the points, simply hold the space bar.

Here is a video which demonstrates that.
The formula is \(z_{n+1}=z_n^2*\frac{z_n-a}{z_n-b}+c\)
where a and b are the blue points in the video.

Quickness of the eye, deceives the mind #Friday #Fractals #FridayFractals #FractalFriday

Nobody can get no sleep, there's someone on everyone's toes

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.

Static in my attic #Friday #Fractals #FridayFractals it's #FractalFriday

A fractal with circles. With the colours of the flag of #Palestine, to reclaim the end of the #genocide in #Gaza.
#geometry #Mathart #fractal #FractalFriday

#FractalFriday meets #FungiFriday meets #Mosstodon.

It's been raining for days on end, which means that the moss is happy, growing shiny and bright green. In this case on a bracket fungus that grows on a tree stump hosting 3 generations of them.

RGB orbit traps