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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Try as I may, I could not decide how to rate today's image, which is a scene in the Hyper-Mandelbrot set. I also am confused as to exactly what this formula does. Sometimes I suspect that it draws two overlapping Mandelbrot sets, but then it comes up with something that does not exist in the familiar Mandelbrot set. For example, consider the parent fractal of today's image. It is obviously closely related to the Mandelbrot set, but it could never be a result of two overlapping M-sets. To start, it has two East Valleys. This could be a result of two identical but slightly separated M-sets, but it has two quadratic midgets where the large period-3 north and south buds should be, and its Seahorse Valley is something entirely new. I named today's image "Eruptive Iterations", since it could be taken as an erupting volcano without too much difficulty. But the most notable feature of the image is its fantastic array of spider-like filaments. It does indeed remind me of the images produced by the type=spider formula. The calculation time of 14 minutes on a P2000 machine is a bit slow. But relief for slowness may easily be obtained on the FOTD web site at: The weather here at Fractal Central got a bit too perfect on Friday, when the humidity moved in and the temperature reached 88F 31C. But heat doesn't worry cats too much, so the fractal cats had a pleasant day despite the heat. And a cooling thunder-shower arrived as night fell. My day was rather busy, and tomorrow will likely be the same. I'll try to post the FOTD on schedule, but there is no guarantee. Until next time, take care, and the more we discover in these fractals, the less we know. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
EruptiveIterations { ; time=0:14:08.82-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=HyperMandelbrot passes=1 periodicity=0
center-mag=+0.28954559806994660/0/2010.667/1/90/\
3.885780586188e-016 params=0/0/0.3/0/0.01/0 float=y
maxiter=5000 inside=255 logmap=90
colors=000ejJdkIdkIckIckIckIbkIbkIalHalH`lH`lH`lH_\
lH_lHZmGZmGZmGYmGYmGXmGXmGWnFWnFWnFVnFVnFUnFUnFToE\
ToEToESoESoERoERoERoESnDSnDTnDTnDUmDUmDVmDVmDWmDWl\
DXlDXlDXlDYlDYkCZkCZkC_kC_kC`jC`jCajCajCajCbiCbiCc\
iCciCdiCdhBehBehBfhBfhBggBggBggBhgBhgBifBifBjfBjfB\
kfBkeAleAleAleAmeAmdAndAndAodAodApcApcAqcAqcArdBqc\
AqcAqbAqbAqaAqaAq`Aq`Aq_Aq_AqZAqZAqYAqYAqXAqXAqX9q\
W9qW9qV9qV9qU9qU9qT9qT9qS9qS9qR9qR9qQ9qQ9qP9qP8qP8\
qO8qO8qN8qN8qM8qM8qL8qL8qK8qK8qJ8qJ8qI8qI8qI7qH7qH\
7qG7qG7qF7qF7qE7qE7qD7qD7qC7qC7qB7qB7qA7qA6qA6q96q\
96q86q86q76q76q66q66q56q56q46q46q36q36q36o47n48m59\
l5Aj6Ai6Bh7Cg7De8Ed8Ec9Fb9GaAH_AIZBIYBJXCKVCLUDMTD\
MSENREOPFPOFQNGQMGRKHSJHTIIUHIUFJVEJWDKXCKYBLY9LZ8\
M_7M`6Na4Na3Ob2Oc1Pd0Pd1Qe2Re3Re4Se4Tf5Tf6Uf7Vf7Vg\
8Wg9XgAXgAYgBZhCZhD_hD`hE`iFaiGbiGbiHciIdjJdjJejKe\
jLfkMgkMgkNhkOikPilPjlhhr }
frm:HyperMandelbrot {; periodicity must be turned off
a=(p1),b=(0,0):
q=sqr(a)-sqr(b)+pixel,
b=(p2+2)*a*b+p3,
a=q,
|a|+|b| <= 100 }
END PARAMETER FILE=========================================
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times.
