Fractal Related Discussion > Fractal Mathematics And New Theories

Random spike minibrots

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pauldelbrot:
As it happens, the base of the M-set's spike is very close to -1.4; the tip, as is well known, is exactly at -2.

So, one "game" you can play to explore a bit is this. Generate a random number between 0 and 0.6, using whatever tool you prefer. Subtract two; set this as the x coordinate in a fractal program set to render the M-set; and set the y coordinate to zero and the magnification to, say, a million. Look for the largest whisker jutting up vertically from the spike and zoom at its point of attachment until a minibrot is found.
Then center on the mini.

A variety of symmetric, almost snowflake-like patterns (but with 4 and 8-fold symmetry, not 6) will surround the minis found by this method.

lkmitch:
Here's one beginning at x = -Phi = -1.6180339887498948482045868343656, y = 0, mag = 1e6. The midget has a period of 62.

https://www.tic.itefi.csic.es/gerardo/publica/Pastor03.pdf

gerrit:
A while ago I made an animation of a bunch of minis in that region:

https://fractalforums.org/index.php?topic=401.msg8172#msg8172

pauldelbrot:
Some minis I found using the procedure outlined in the first post.