END OF AN ERA, FRACTALFORUMS.COM IS CONTINUED ON FRACTALFORUMS.ORG

Here's an idea that I've just started playing with:

init:
  iter=0
  z=0
loop:
  iter=iter+1
  rot=cos(iter)+i*sin(iter)
  z=z^power+rot*pixel
endloop

Modifications can be made to include a slider from 0 (regular Mandelbrot calculation) to 1 (full rotation effect) or to alter the amount of rotation each iteration.

David-  I PROMISE I'll try it, but I can't say WHEN!  Things are a little hectic for Bunny & me right now- the headlines are catching up to everyone, so we're struggling a bit to maintain life as we know it.  Hope things are more comfortable 4 U.

And...a...later (if there is one).

AFAIK anything that is disconnected in n dimensions can become connected in n+1 (or higher) dimensions - I don't know a stochastic proof for this but it seems "obvious" enough

The formulas in the zip are just text files in disguise - i.e. load them into any standard text editor and you should be able to read them OK.
For a quick and easy comprehension of how most UF formulas work just look one or two in mmf.ufm first, once you have the general idea then following them shouldn't be a big problem

That's essentially correct, but doesn't cover any of the UF5 class-based formulas (*.ulb) and of the others some functions introduced in UF4 and UF5 are not supported but I think any for UF3 or UF2 will work perfectly in ChaosPro.

dwsel-  I'm a really old-fashioned guy, I guess: I use FractInt (and they all moved away from me on the bench...) and write formulae in Notepad (clean & simple).  Maybe other progs may offer more bells & whistles, but I try to keep it simple while I don't really have time to orient myself to their use.

David-  It's reassuring that you also view the greater chances of connectedness as more dimensions are available.  I felt it early on, and tended to observe it in practice later.  I'm comfortable enough to piece together a 3-d view from 2-d slices, but I'm sure some others may find it hard to visualize.  But I wonder if there is some object so hopelessly disconnected in 3d or less that it requires more than 6 or 8 dims to be connected in one piece, although we would not be able to visualize it in any way we're used to...and then, of course, there are String Theorists, (not to mention Theologists,) expert at finding questions that can't be proven one way or the other...I wouldn't know where to begin reading a proof, much less writing one!

'til next time,

Later...

Not that I'm back exactly, but-

(This time of year, I'm usually building while not travelling to do building, most often with wood, less with stone, but it's all-consuming, & makes me a dull boy...)

Whenever I get a chance, however, I'm still exploring the many wierd new bugs with multiple multibrot-power-types that one can obtain by generalizing the method I've previously described in this thread.  My formula D32g yields an index set (pic 1 below) that contains M32, M8, & M2* power types, simply connected.  The function is f(z)->((((((z^2)c-1)^4)-1)^2)-1)^2**, for those who'd like to look for themselves.  The 2nd pic is of the whole julia set for a location ctrd. in pic 1, where there is a secondary mini of an M2.  The 3rd pic enlarges the center to show a J4 feature there, that ALWAYS appears about the origin in dendritic j-sets for this function, there at the origin, but nowhere else, nor in the index set.  Try to beat me to explaining why it's there...(it's easy, because I don't have a clue, nor any time to think about it)

But I thought I'd try to stay in touch...

Later!


_____________________
*  M2 is the designation for the "standard" M-set shape, as opposed to Multibrots of other powers.
** Oops!  Sorry, folks: I had originally misreported what was actually the formula for D32h (not shown): f(z)->(((((z^2)c-1)^8)-1)^2)-1, in which the index and Julias both contain 32, 4 & 2 power features, also not suggested by the function in any obvious way.  Also interesting to look at, however...

Intuitively I'd say anything disconnected in <n dimensions could be connected in n or more - I'm guessing there's a topological proof of this, but I've never studied topology.

Update-  I've been looking at multiple power shapes for odd powers again, with some work on combining both odd & even powers.  It seems that when it comes to powers, any combination can be made as long as only one of them is prime.  I'll try to show pix of other traits soon.

Later!