David.

Maybe it would be useful for what you are trying to do also. Here is a patch that I think does what you described. One note: inside the patch the states of the iterations are saved to a globally accessible table (10 values), but it doesn't work because if you address it at index 0, it doesn't always give you the last state. It would be excellent if the indexes 0 1 2 ecc.. would always return the last state, second to last, third to last ecc..but I don't know how to do it.

fractals.iterations.zip

Are these the same objects that were in extended?

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

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?

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

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.