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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: We have another new formula today, so be sure to copy it into one of your formula files. The formula draws oblique slices of (-Z)^n Julibrots. I named the image "Pipefish Valley". A pipefish is a kind of seahorse without the curly tail, and today's image is a near-Julia set of the large valley of the (-Z)^(1.125)+C Mandeloid. This valley cannot honestly be called a Seahorse Valley, since it has no curly-tailed seahorses, but it is interesting nonetheless, and especially so in its near-Julia aspects. The pure Julia set of the valley is a rather drab empty figure-8 shaped figure, but by centering the view on the inside of the upper arm of the valley and rotating the view 2-1/2 degrees toward the Mandelbrot orientation, I managed to make a rather interesting image of it. A good part of the scene consists of 'inside' stuff made visible by the 'bof61' inside fill. The coloring adds an unusual textured smoothness to the scene. I credited myself the usual 1/2 point for the coloring, and rated the image at a 6-1/2. The image is a slow one, taking over 41 minutes on the fast machine, so I recommend viewing it on the FOTD web site at: A typical midwinter day prevailed here at Fractal Central on Tuesday, with cold winds, lots of gray clouds and a temperature of 34F 1C. And the forecast is for things to become even more winterish over the next several days. The fractal cats were too busy sulking at each other to notice the weather. My day was about average. The next FOTD will appear in 24 hours. Until then, take care, and if God, who is never wrong, tells me the future, will I still have the free will to avoid the things he tells me will happen? Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
Pipefish_Valley { ; time=0:41:38.66-SF5 on P4-2000
reset=2004 type=formula formulafile=allinone.frm
formulaname=SliceJulibrot5 passes=1 periodicity=10
center-mag=-0.344371/0.0122124/1.180338 inside=bof61
params=87.5/87.5/87.5/87.5/-0.7362027083/0.04/0/0/\
1.125/0 float=y maxiter=30000 outside=tdis logmap=12
colors=000YT0WTBWSAVSAURAUR9TQ9SQ9SQ9RP8QP8QO8QO7P\
O7PN7ON7NM6NM6MM6LL5LL5KK5JK5JK4IJ4HO4GM3HJ4IF4IH4\
JI4JK4KL5KN5LO5MQ5MR5NT5NU6OW6OX6PZ6Q_6Qa7Rb7Rd7Se\
7Sg7Th7Uj8Uk8Vm8Vn8Wp8Wq8UnDTlHRjLQhQOfUNdYLabK_fI\
YjHWoFUsESwFPvFNuFLtFJtFHsFFrFDqFBqF9pF7oE4qF5oG5m\
G5kH5iI5gI5eJ6cJ6aK6_L6YL6WM6UM7SN7QO7OO7MP7KO6GP7\
IP7JP7KQ7LQ7MQ7NR7OR7PR8QR8RS8SS8TS8UT8VT8WT8XT9YU\
9ZU9_U9`V9aV9bV9cW9dWAeWAfYAgZAhcAihAjmAkrAnvBqzMt\
zUwzUzwXzrNzmBzjByf9wcAtaBq`CnZClYDiYEfXEdWFaWG_VH\
ZVHXUIVTIVTHUSHTRHTRHSQGQQGPPGPOGOOINNKNMMLMNJLPIL\
RGKSEJUDJVBIW9HW8HX6GY4GY3FZ4KZ5PZ6UZ7ZZ8cZ9hZAmZB\
rZBvZCzZDzZEzZFzZGz_Hz_Iz_Jz_Jz_Kz_Lz_Mz_Nz_Oz_P9_\
Q8_R8_R8_S8_T7`U7`V7`W7`X6`Y6`Z6wZ5w_5w`5wa5wb4wc4\
wd4we5wf4we4we4we4we4we4we4wemwzmwzmwzmwzmwzmwzmwz\
mwzmwzmwzmwzmwzmwzmwzmwzmwzmzzmzzmzzmzzmzzmzzmzzmz\
zmzzmzzmzzmzzmzzmzzmzzmzz }
frm:SliceJulibrot5 {; draws slices of (-Z)^n Julibrot
pix=pixel, u=real(pix), v=imag(pix),
a=pi*real(p1*0.0055555555555556),
b=pi*imag(p1*0.0055555555555556),
g=pi*real(p2*0.0055555555555556),
d=pi*imag(p2*0.0055555555555556),
ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g),
sg=sin(g), cd=cos(d), sd=sin(d),
p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd),
q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd),
r=u*sg+v*ca*sb*cg, s=v*sin(a),
c=p+flip(q)+p3, z=r+flip(s)+p4:
z=(-z)^(p5)+c
|z|<=9 }
END PARAMETER FILE=========================================
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times.
