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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: We seem to be developing a theme for the month of June. I had no intention of having two 'theme' months in a row, but sometimes fractals have a will of their own, and a theme of midgets in the many Z^(1.5)+C fractals seems to be developing. Today's image is the third consecutive scene in the set of fractals created by the formula Z^(1.5)+C. As the lengthy real(p2) parameter shows, the parent fractal was found by the evolver feature. I could have rounded off this parameter to -46.7 with little change in the resulting image. Fractals with exponents in the X.5 range are the most prone to the type of discontinuities that fill today's image. Fractal discontinuities decrease in significance as the exponent nears integer values, and vanish entirely when the exponent is an integer. I normally use the <floor> function with the MandelbrotBC1 formula, but for a change, I used the <recip> function in today's image. In today's image, which lies in the most-discontinuous range of exponents, the attractive symmetrical patterns that surround midgets in the classic Mandelbrot set are totally absent. Today's half-midget is surrounded by a kind of star-burst with an obvious break in the upper part. This break totally destroys any pretense of symmetry, though it does make an interesting feature. To add more interest, I rendered the image with the outside set to <fmod> and the proximity set to 0.5. The other outside options also make interesting variations of the basic scene, and are worth checking. I named the image "Unity and a Half" as a description of the exponent. I could rate the final result at only a 6. The rating is held down by the coloring, which could have used a bit more work. At least, the render time of 6 minutes is reasonable. The download of the finished image file is even more reasonable. That download can be found at: Another perfect day here at Fractal Central on Monday produced perfect cats. The not-quite-dynamic duo spent the better part of the day in their porch chairs, watching the world, enjoying the temperature of 73F 23C, and remembering the days when they were actually dynamic. Today, unfortunately, is starting cloudy, with rain promised by afternoon. For me, it will be just another workday. Until next time and next fractal, take care, and sometimes fractals are not all they're cracked out to be. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
Unity_and_a_Half { ; time=0:06:08.50--SF5 on a P200
reset=2002 type=formula formulafile=allinone.frm
formulaname=MandelbrotBC1 function=recip passes=1
center-mag=-0.73254313764763500/+0.180334958341697\
00/4.605696e+007 params=1.5/0/-46.74114200262459/0
float=y maxiter=4200 inside=0 proximity=0.5
outside=fmod symmetry=none periodicity=10
colors=000CvNBnPBfRBZTASVAKXACZA5`WSZpnYokZnhZmeZl\
bZk_ZjX_iU_hR_gO_fL_eI_TFYHCXMIYQNYVSYZXYbaYgfYkkY\
opYkk`gfccae_XhXSjTNmPIpLDrH8uE4wF6rF7mG9hGAcO8TV6\
Ia47WGFQSMKcUEo`9zgBxcCv`DtYErVGpSHnPIlMJjJKiGPlJU\
nMZpPcrShtVmvYks_ipagmcfjedggbdi`ak_ZmYWoWTqUQsTNu\
RPrPQoOSmMTjLUhJWeIXcGY`E_YD`WBaTAcR8dO7eMBcOEaPI`\
RLZSOYTNTRMPPWnaSoYOpVJqRFrNBsK7tG3tD5qE6nF8lG9iHB\
gICdJEaKF_KHXLIVMKSNLPONNPOKQPIQY9Kf1Fg7DgCCgIBhNA\
hT9hY8ic7ih6im5ciAYfFScJN`OHYTBVX5Sa0Pe3Of6Og9OhBO\
iEOjHOkJOkMOlPOmROnUOoXOpZOp_Kl_Hh_Dd`A``6X`3T`0Qb\
2Td3Ve4Xg6_h7aj8ckAfmBhoCjpEmrFosGquItvJvxKxyLzwOy\
vQxuSwtVvsXurZtqaspcroeqnhpmjollnkomjqlislngkrWkUg\
W6sGBcSGOcL8nODmQHlTMkVRjYWi__iadhdhgfmfiqekudiwib\
vkbti_odWj_TfVQaQMXLJTGFOBCJ69F1BE2CE3ED3FD4HC4IC5\
JB5LB6MA7OA7P98R98S89T89SBBSDCSGESIFSKHRNIRPKRRLRU\
MRWOQZPQ`RQbSQeUQgVQiWJpR }
frm:MandelbrotBC1 { ; by several Fractint users
e=p1, a=imag(p2)+100
p=real(p2)+PI
q=2*PI*fn1(p/(2*PI))
r=real(p2)-q
Z=C=Pixel:
Z=log(Z)
IF(imag(Z) > r)
Z=Z+flip(2*PI)
ENDIF
Z=exp(e*(Z+flip(q)))+C
|Z| < a }
END 20.0 PAR-FORMULA FILE==================================
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