Mike Frazier wrote:
In my recent post all the structures that had an odd number of arms had no minibrot and the ones with an even number of arms did (except a spiral). I am not sure if that is a general conclusion for the whole Mandelbrot set of just the tiny area I looked at.
To play the Smart Aleck here: What you meant was that spirals with even arms do not have minibrots of roughly the same size as the ones with odd number of arms - since the whole border of the M-set consists of an infinitude of minibrots (besides Misiurewicz points, which are accumulation points of said minibrots), therefore also the even armed spiral do contain minibrots. Two quotes by Michael Frame (http://classes.yale.edu/fractals/): "The Misiurewicz points are scattered throughout the boundary of M: every circle centered at every boundary point encloses infinitely many Misiurewicz points." "The boundary of the Mandelbrot set is a very complicated place, because in addition to the Misiurewicz points, every circle centered at every boundary point encloses infinitely many centers, hence infinitely many copies of the Mandelbrot set." However, I have no idea either, if there's any significance to the difference between even- and odd-armed spirals.
I have explored some more since the post and I found a few more interesting tidbits. When zooming in on one of the even armed structures I noticed that it caused a new feature to get inserted between some familiar structures that I had seen before. At the start of the zoom it caused the whole repeating feature set to get reset to the beginning. One result of the reset to the beginning was that I passed the original structure that I zoomed in on again. If you took the "detour" a second time it added a second feature exactly like the first right after the first. Seeing the pattern, I could add as many features of this type to the fractal as I wanted by taking the same detour over and over as I zoomed in. You can also pick to add one feature type then a different feature type by picking the detours as you zoom in. It seems possible to customize the fractal by adding the shapes you want after finding out what each kind of detour does.
People do that already. If I'm allowed to throw a few links at you: A screenshot by James W. Morris from mdz (his own program, for Linux). He's obviously checking different zoom routes here: http://www.fractalforums.com/index.php?action=gallery;sa=view;id=4434 And stardust4ever with, to use your expression, customized Mandelbrot images: http://www.fractalforums.com/index.php?action=gallery;sa=view;id=1983 Here's an image illustrating his descent into the depths of the M-set: http://stardust4ever.deviantart.com/art/Making-X-Fractals-155341193 Not to forget Jonathan Leavitt, who seems to have been the first who stumbled onto the reverse bifurcation effect in the late 90's. Below are the two Fractint params that were posted here on the list in 1998 by his friend Jonathan Wolfe: hournozo {;by Jonathan Leavitt, 1998 ;~34 hours at 233 MHz ;10^76 deep ;mapname is verica reset=1910 type=mandel center-mag=-1.7494731962100301093025521422405488627568109828713567987988\ 6197663174423971559038/4.65032129863512237555970979220949188044571977348\ 3014616191461119829263616e-9/8.944236e+075/1/-97.499 params=0/0 float=y maxiter=6666 inside=0 colors=000hkm<22>zzhzzhzyh<21>uieuhetgdtfdsfdred<36>WPbVObVObVOb<61>65E5\ 4D54D43C43B<9>116115004003002000000000<13>00M00O00O<57>dgmehmehmfimgimhj\ m } vlernfa {;by Jonathan Leavitt, 1998 ;~50 hours at 233 MHz ;10^93 deep ;mapname is girustic reset=1910 type=mandel center-mag=-1.7498797637233036250531541288085660873308706813150940739022\ 160997776415279220633903858035532704437/3.711275390023365538060136900393\ 27923739521658716180513365112109254521643684694157319e-15/1.676666e+093/\ 1/-115 params=0/0 float=y maxiter=11111 inside=0 colors=000GGJ<8>LLOLLPMMQNNRNOS<39>dpxdqyerzfsz<26>yyzzzzzzyzzy<45>zzczz\ czzczycyxb<47>eHLeGLdGLcGK<31>211000000<32>GGJ } Regards, Gerald