For the sake of the experiment: I have built the Mandelbrot Iteration with BW Math

[] Peter:H []

It is quite easy to implement the basic formula x(n+1) = x(n)² + c, where x and c are complex numbers. c = a + bi, where bi indicates the imaginary part of a complex number.

Tricky is the recursion part that is where the result of one computation feeds as input into the next computation, so we get a sequence of values X(1), X(2), ..., X(n). I solved this with long delays... and a some more tricks.
Currently demo projects "long delay" has actually a long delay time so that you can follow what happens by reading the value displays when the patch works.

Currently this thing is in raw form. It does not implement the breaking condition of the mandelbrot iteration which should stop when X(n) escapes to infinity. I currently only want to use it for so called complex attractor, i.e. a sequence of x(n) which repeat over and over again. this happens for some points in the "black" area of the mandelbrot set. But it's not all of the black points only points to the outter bulbs ... try out here if you want to see what I mean https://openprocessing.org/sketch/77478.

Right now the patch is set up with values of c = a + bi in Section "Your Input goes here" with a cycle of 2. So the values in the XY to the right jump around between two positions. There are other more complex attractor sequences but I wasn't able to find one in the short of the time.
Feel free to come up with values of a + bi on your own and share here.

If you for instance dial in a = -1.10 and bi = 0.25 you see the point first jumping around and then it escapes to infinity, meaning the values get bigger and bigger with each iteration.

How to start the Iteration: Hit the Trigger "Start/Stop" (left top). If you don't see values in the x/y panel to the right change then you might need to hit start a second time.

Use of the Patch: I don't want to see this patch copied in any arbitrary monetized youtube video or patreon content. thanks. Use it for your experiments and share your findings here.

Bitwig Math Mandelbrot Iteration.png

The give shows how the values cycle for settings a=-0.49 and bi = 0.55

Bitwig Math Mandelbrot animated.gif

[] Peter:H []

Found values for cycle lenght 3 (source https://mathhelpforum.com/threads/fixed ... et.135085/)
−1.754877667 + 0i,
−0.1225611669−0.7448617670i,
−0.1225611669+0.7448617670i,

So if you dial in for a = −0.1225611669 and for bi = −0.7448617670 and start the iteration the point in the x/y panel jumps to 3 locations over and over again.

More values, let's try
a=-0.69 and bi = 0.28
a=-0.1 and bi = 0.8 (cylce period is 3)
a=-0.49 and bi = 0.55 (cycle period 5)
Values discovered by the help of: https://mathigon.org/course/fractals/mandelbrot

[] Peter:H []

And here's a picture which shows the periods of attractors: https://upload.wikimedia.org/wikipedia/ ... loured.png.
It get's up to 29 points that repeat in a cycl. Who can come up with the parameters?

[Tj Shredder]

That looks very interesting. Especially if you start to modulate those values. It creates interesting chaotic movements, even if you come back to the old values.
Now we want to turn it into sound...

[ollie.rollover]

Wow.