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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Today's image looks somewhat like a nuclear explosion. It is actually a picture of the Julia set of the Z^(1.25)+C Mandeloid as it exists only one level up the spiral. Or perhaps I should say 2.14159... levels down the spiral. The number PI works better as a ground level. The interesting Julia sets that can be created with the JuliaBC formula are very easy to find and they are literally endless in number. And, as today's 24-second render time shows, they are lightning fast. I'll post a few more low-order Julia sets before returning to the hoard of old, forgotten, mostly useless formulas. I want to check the Julia sets of a few of the square-root-of-two Mandeloids. Since today's fractal basically found itself, I could rate it no higher than a 5. The name merely indicates that it is the fourth in the series of similar images. (The first in the series was not an FOTD.) For the convenience of those with over-qualified computers, the completed image is available on the FOTD web site, which may be accessed at: A chilly blustery day Wednesday produced just enough sun to keep the cats in a neutral mood as they lurked in the yard. With the work still caught up, my mood was good. Today is starting sunny but chilly, leading me to expect another marginal day for the cats. The next FOTD will appear in 24 hours. Until then, take care, and be with it. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Julia_Variation-4 { ; time=0:00:24.06--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=JuliaBC center-mag=-0.0612658/0.043239\
/0.3908483/1/-90/3.88578058618804789e-016
params=1.25/0/1/0/0.09428/-0.0025/0/0 float=y
maxiter=1000 inside=0 outside=real periodicity=10
colors=000HL8FM8DN7BO79P67Q65R53S51T54U77V89WACXBF\
YCHZEKaFNcGPfIShJUjKWfNYcQ_`T`YWbUZdRahOcmLfrHivEl\
zBoz8rz5tz6qz7nz8kz9hzAevBbrC_mDYhEVcFSZGPUHMQIJOJ\
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qzHwzJqzKmzLczNYzOYwPYrRYmSYiUYhVYgWYeYYdZYc_Yb`ad\
adfchidkkfongrphurbkoYamTSjOIhJ8fNAgQChTEiWGiZIjaK\
kdMlgOljQmmSnpUnlTkiThfSecSb_R_XRXUQURQROQOMPNKPNI\
PNHONFOMDOMCNMANM8NL7ML5ML3ML2ML4NO6NR8OUAOWCOZEPa\
GPdHPfGQbFQ_FRWERTERQDSMCSJCTFBTCBT9EU8GV8IW8LX8NY\
8PZ8SZ8U_8W`8Za8`b8bc8dc8eaAe_BeYDeWEfUGfSHfRJfPKg\
NMgLNgJPgHQhFShEThCVhAWi8Yi6Zi4`i3ak8YlDUnIQoNMpSI\
rXEsaAte6pf7mg8ig9fhAciA_iBXjCUkDQkDNlEKmFGmGDnGAo\
H6oI3pJ0pJ1lK1iL1fM1cN1`N1YO1VP1SQ1PR1MRGU`V`jhgtg\
drfbpf_neYldWjdThcRfcOdbMcaKaaH_`FY`CW_AUZ8SZ5QY3O\
Y1NW2RV2UU3YT3`S4dR4gQ5kP5nO6rN6uM6xP7tR7pT7mV7iX7\
fZ7b`7Zb7Wd7Sf7PhANiDLjGJ }
frm:JuliaBC { ; Formula by Andrew Coppin
e=p1, p=real(p2)+PI, q=2*PI*floor(p/(2*PI)),
r=real(p2)-q, C=p3, Z=Pixel:
Z=log(Z)
IF(imag(Z)>r)
Z=Z+flip(2*PI)
ENDIF
Z=exp(e*(Z+flip(q)))+C
|Z| < p4+100 }
END PARAMETER FILE=========================================
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times.
