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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image shows a squared Mandelbrot midget. Yes, I know that the Mandelbrot set results from squaring Z, but today's unlikely formula squares the entire Mandelbrot set. More correctly, the formula scrunches and stretches the set. And it changes the entire set into a diamond shape, along with its midgets. It wreaks total havoc with the normally placid iteration bands. Today's image shows one of the midgets deep in East Valley of the large midget on the negative stem of the parent M-set, which itself has been changed into a diamond. To add a bit of depth, I rendered the image with the outside set to 'tdis'. As for the formula itself. It was not written by me, and I have no idea what the original author was trying to do. I named the image "Diamond in the Rough", and rated it at an average 5. I could not rate it higher because too little effort was put into adding diamond-like sparkle. The name is a bit misleading, as diamonds in the rough have an irregular shape. They do not take on the typical diamond shape until they have been carefully cut by a master craftsman, which is one reason why they are so costly. The fractal diamond's almost non-existent sparkle may be seen by running the attached parameter file and waiting a few minutes, or by downloading the finished GIF image from the FOTD web site at: The sunny 73F 23C weather on Monday was perfectly perfect here at Fractal Central. The cats were near perfectly happy. I cannot claim absolute happiness for the cats because who knows what goes on in a cat's mind. But with the work under control, my day was satisfactory. Today is starting the same as yesterday. I expect good things. Until tomorrow, when the next FOTD appears, take care. The Halloween hauntings have ended; the saints have arrived. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
DiamondInTheRough { ; time=0:08:47.12--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=C4G passes=1 center-mag=-1.74996259251\
672100/0/7.855169e+008/0.7484 params=1/0.8 float=y
maxiter=16000 inside=0 outside=tdis
symmetry=xaxis periodicity=10
colors=000Lj`Ji_IhYHgWFfVEeTCdRBcPAbO8aM7`K6_J4ZH3\
YF2YE4XF6XG7WG9WHAVHCVIDVIFUJGUJITKKTLLSLNSMOSMQRN\
RRNTQOUQOWQPWPPXPQZORYORZNSYNSZNTYMT_MU`LUbLVcKWcL\
VbMUaNT_NSZORYPRWQQXQPYROYSNYTMYTMYULWVKWVJVWITXHS\
YHRYGQZFO_EN`DM`CKaCJbBIcAGc9Fd8Ee7Cf5De7Ed8FcAGbB\
HaCH`EI_FJZGKYILXJLXKMWMNVNOUOPTQPSRQRSRQUXmLVlKUk\
KTjKRiKQhJPgJOfJMeJLdJKcIIbIHaIG`IF`II_JK_JN_JP_KS\
_KU_KW_KZZL`ZLcZLeZMhZMjZMlZMAKS9JR9IR8IQ7HQ7GP6GP\
5FO5EO4EN3DN2EM3DN3CN3CN3BO3BO4AO4AP49P49P48Q58Q57\
Q57R56R56R65S65S64S64T63T63TA5UD7UG8UJAUMCUPDUSFVV\
GVYIV`KVcLVfNVgOViOVVTBUWETYHS_KScLRaMQ_NPYOOXPNVQ\
NTQMRRLQSKOTJMUIKVMEUIJVEOWATX3_V7XYBU_FSbJPdNNgRK\
iVHkZFnbCpfAsj7uo4yn5wm5ul6sl6qk7pj7ni8li8jh9hg9gf\
AefAceBadB_cCZcCXbDVaDT`ER`EQ_FOZFMYGKYGKYGJZJMZMP\
ZPRZSUZVW__Z_da_hc_mf_rh`vkmzzmyzmxzmwzhvwcutZtqXs\
pWrnUqlTpkSoiQngPmeNldMkb }
frm:C4G {; p1 is (plus or minus) 1 or i
x=real(pixel), y=imag(pixel)*p1
a=b=0:
a1 = a^2-p1^2*b^2
b1 = 2*a*b
a=a1+x, b=b1+y
z = sqrt(a^2 + b^2)
z < 4 }
END PARAMETER FILE=========================================
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