does anybody know how to write for example this formala into the expr object: c=(((c²+c)²+c)²+c)²+c ? its the fourth iteration of a fractal. this is the first iteration: c=c and this is the second c=c²+c. my second question is if there is a formula to get the first, secont, third iteration etc.. i hope my mathematical terms are correct and understandable

@mnb thanks for the hints. you are right, the iterations should work like that:
and i am also sure you are right with the complex numbers as well. i read somewhere that i have to use the x y values of a circle as the input for the expression to create mandelbrot figures, but it didnt work out so far i just start to understand the fractal and the expr thing.

i have some interesting results with the chaos library. this one is from the lorenz object. still i like to understand how to make expressions like that.

@Jona Did you see this thread? There are some interesting patches in there.

https://forum.pdpatchrepo.info/topic/4646/complex-differential-equations-calculated-by-pd/25

@weightless thanks, very interesting thread. i tried the manit patch, this is a result: but its not easy to find nice variations. in this regard the lissajous formala is very thankful. there is an interesting remark from @katjav: "I found it impossible to find an interesting fractal 'by hand' though. Everytime when a pattern sounds interesting, it's flying to the stars and reset, being not part of the Mandelbrot set. The logistic map function is much easier to handle, like Elaine mentioned in her thesis." i have to admit perhaps my idea to create easily musical patterns from fractals was a little bit naive, but who knows.

@Jona I tried to implement the manit patch into your sequencer too but couldn't get it to show anything! Would you mind sharing the patch?

Perhaps there are other, more varying formulas that lend themselves better to musical explorations in this fashion. In Elaine's paper it is discussed how to use complex chaotic functions, so perhaps the manit patch could be adapted for other formulas?

@weightless here is the patch: manit-seq.zip

@Jona Thanks a lot! I will have a look and maybe learn something from how you plot the values with the data structure.

@weightless this is the part of the patch that plots the values. it chooses the $0-draw element of the $0-array array and then sets the x and y value. each step bangs every existing element. c is the color of the element. if you have a question about the plotting i will try to answer.

and i'm not exactly sure if the 'classic mandelbrot-set series' yields any musically interesting results, but
i am quite sure that it only produces usable results for carefully chosen values of c (on the border of the mandelbrot set where it neither converges nor diverges, at least not so quick...).

maybe simple real-valued recursive functions are more fun. the idea is to blow up a value (multiplying, adding constants, whatever), then wrap it to a range, and feed it to the next iteration. like the classic gingerbreadman, hopalong etc. fractals. linke in the attached example. fractalmelody.pd

@mnb thanks, nice patch. that sounds very interesting. i will have to learn about that.

@mnb the recursion trick with the sine function is nice. i tried to create a longer slow development with your formula (its quite repetetive in the beginning):

@Jona The dream-seq is now also working:

dream-seq.pd (updated)

The formula is the "Kings Dream" fractal taken from http://softology.com.au/tutorials/attractors2d/tutorial.htm. There are some more interesting formulas on that page.

Some parameters give decent results. For some parameter combinations it is better to turn motion off so it would not converge against a less interesting figure.

Update:
Now there is a toggle "symmetry". When it is checked the parameters on the left will also set the parameters on the right. The right ones are still free. Also changed the plot to bezier curve. It doesn't plot through the nodes, but is still nice.

@ingox very nice. more possibilities than i thought