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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Yes, I realize that I'm late. It's actually 8:15am Sunday morning here at Fractal Central, and I'm just now getting around to writing and posting the FOTD for today. My excuse is that I was busy all day yesterday and last evening painting walls in the new soon-to-be Fractal Central. Another peculiarity is that I have attached two different versions of the parameter file of today's FOTD. Version-1 refers to a separate arches.map file for the color information; version-2 has the color information included in the normal manner. I have attached the .map file required by version-1 to the bottom of this letter. Running version-2 of the parameter file can be done in the normal manner, but the colors will be significantly incorrect (at least on my monitor). Version-1 of the parameter file will give more accurate colors, but before this can be done, the arches.map file must be edited from the bottom of this letter and saved in your Fractint directory as a text file named < arches.map >. The image itself was created by number 12 in my series of 12 MandNewt formulae, all of which are distortions of the Ikenaga function. I named the picture "Mandelbrot Arches" when I noticed the group of arch-like features spanning the screen before a multi-colored-sky background. I considered all aspects of the image before rating it an above-average 7. It is this exceptionally smooth background that causes the inaccuracy when the colors are recorded in the normal manner. The background should have virtually no visible bands, but this happens only when version-1 of the parameter file is run. Running version-2 causes unintended bands to appear. The difference is small, but it is there. This is not a bug in the program; it is simply an unavoidable result of squeezing the color information into the very compact 'parameter file' format. Both versions of the parameter file run in just under 13 minutes on a 200-mhz Pentium, though it will take a few minutes longer to get set up to run the more accurate version-1. Time can be saved by giving Paul and Scott a chance to run the image and post it to their web sites at: The fractal weather today was sunny but quite cold and blustery, with an afternoon temperature near freezing, which kept the cats safely indoors. They seemed to accept their confinement unusually well, probably because I gave them an extra treat of tuna. Well, I see that it's now time to get started on another day of work at the up-and-coming new Fractal Central. It will take several weeks to finish the new place, so don't worry if the FOTD is occasionally late in the next month or so. All FOTD's will eventually appear. And I'm about to disappear. Until next time, take care, and see you in about 16 hours. Jim Muth jamth@mindspring.com |
START 20.0 PAR-FORMULA FILE================================
Mandelbrot_Arches1 { ; time=0:12:47.53 -- SF5 on a P200
reset=2001 type=formula formulafile=critical.frm
formulaname=MandNewt12 passes=1 center-mag=0.576401/\
0.549019/5.615454 params=-2.11485/5.39629/1.36453/-5\
.27693/-1.42156/-3.25674 float=y maxiter=250
inside=bof60 logmap=yes periodicity=0
colors=@arches.map
}
Mandelbrot_Arches2 { ; time=0:12:47.53 -- SF5 on a P200
reset=2001 type=formula formulafile=critical.frm
formulaname=MandNewt12 passes=1 center-mag=0.576401/\
0.549019/5.615454 params=-2.11485/5.39629/1.36453/-5\
.27693/-1.42156/-3.25674 float=y maxiter=250
inside=bof60 logmap=yes periodicity=0
colors=000QQkRRjRTjSPgTGW00HZBUVZh<3>ZbfZdf_ee<2>bhd\
fjfdke<11>MIVKGUJDT<3>C3P<8>H9UIAVIAW<3>KEYLFYLGZMHZ\
MH`<3>OKaPKbPLbQLcQLcPLdOMc<3>UPdWQdXRd<3>bYcdZce_c<\
3>kcbmdboebofb<3>ujawkaxla<9>omfnmflmg<16>UmoTmpSmpR\
mqQmq<2>NkuMksNjvMjuLjsLjqKirKimJijJihIhhHhd<2>Gg`Fg\
WFgUEfVDfUDfNCfLCfJBfH9fG<4>EfEEgEFgE<23>Zs8Zt8_t7`u\
7au7<2>bv7XrLRnZLjlHgy<28>4Vy4Vy4Vy<2>2Ty2Ty1Rz<3>2V\
x2Vw2Ww2Xw92t<18>PPk
}
frm:MandNewt12 {; Jim Muth
z=g=pixel, a=real(p1), b=imag(p1), c=real(p2),
d=imag(p2), e=real(p3), f=imag(p3):
h=z^a+(g-1)*(z-b)
j=c*z^d+g
z=z-e*h/(f*j),
.0000000000000000000000000000005 <= |h|
}
END 20.0 PAR-FORMULA FILE==================================
START arches.map FILE======================================
0 0 0
104 104 192
108 108 188
108 116 188
112 100 176
116 64 128
0 0 68
140 44 120
124 140 180
128 144 176
132 148 176
136 152 176
140 156 172
140 164 172
144 168 168
148 172 168
152 176 164
156 180 164
172 188 172
164 192 168
156 184 164
152 172 160
144 164 156
140 152 152
132 144 148
124 132 144
120 124 140
112 112 136
108 104 136
100 92 132
96 84 128
88 72 124
80 64 120
76 52 116
68 44 112
64 32 108
56 24 104
48 12 100
52 16 104
56 20 108
56 20 108
60 24 112
60 28 112
64 28 116
64 32 116
68 32 120
68 36 120
72 40 124
72 40 128
76 44 128
76 48 132
80 52 132
80 56 136
84 60 136
84 64 140
88 68 140
88 68 148
92 72 148
92 76 148
96 76 152
96 80 152
100 80 156
100 84 156
104 84 160
104 84 160
100 84 164
96 88 160
104 88 164
108 92 164
116 96 164
120 100 164
128 104 164
132 108 164
140 112 160
144 120 160
152 128 160
156 136 160
164 140 160
168 144 160
172 148 160
180 152 156
184 156 156
192 160 156
200 164 156
208 168 156
208 172 156
216 176 152
220 180 152
228 184 152
232 188 152
240 192 152
244 196 152
244 200 152
240 200 156
236 200 156
232 200 160
228 200 160
224 200 164
220 200 164
216 200 168
212 200 168
208 200 172
204 200 172
196 200 176
192 200 176
188 200 180
184 200 180
180 200 184
176 200 184
172 200 188
168 200 188
160 200 192
156 200 192
152 200 196
148 200 196
144 200 200
140 200 200
136 200 204
132 200 204
128 200 208
120 200 208
116 200 212
112 200 212
108 200 216
104 200 216
100 200 220
96 196 228
92 192 232
88 192 224
92 188 236
88 188 232
84 188 224
84 188 216
80 184 220
80 184 200
76 184 188
76 184 180
72 180 180
68 180 164
68 180 156
64 176 152
64 176 148
60 176 128
60 176 120
56 172 124
52 172 120
52 172 92
48 172 84
48 172 76
44 172 68
36 172 64
40 172 60
44 172 60
48 172 60
52 172 60
56 172 56
56 176 56
60 176 56
64 180 56
68 180 52
72 184 52
72 184 52
76 188 52
80 188 48
84 192 48
88 192 48
88 196 48
92 196 44
96 200 44
100 200 44
104 204 44
108 204 40
108 208 40
112 208 40
116 212 40
120 212 36
124 216 36
124 216 36
128 220 36
132 220 32
136 224 32
140 224 32
140 228 32
144 228 28
148 232 28
152 232 28
156 236 28
156 236 28
156 236 28
132 220 84
108 204 140
84 188 196
68 176 248
64 172 248
64 172 248
60 168 248
60 168 248
56 164 248
56 164 248
56 164 248
52 160 248
52 160 248
48 156 248
48 156 248
48 156 248
44 152 248
44 152 248
40 148 248
40 148 248
36 144 248
36 144 248
36 144 248
32 140 248
32 140 248
28 136 248
28 136 248
28 136 248
24 132 248
24 132 248
20 128 248
20 128 248
16 124 248
16 124 248
16 124 248
12 120 248
12 120 248
8 116 248
8 116 248
4 108 252
8 112 248
8 116 248
8 120 244
8 124 244
8 124 240
8 128 240
8 132 240
36 8 228
40 16 224
44 20 224
48 24 220
52 28 220
56 32 216
56 40 216
60 44 212
64 48 212
68 52 212
72 56 208
72 64 208
76 68 204
80 72 204
84 76 200
88 80 200
88 88 200
92 92 196
96 96 196
100 100 192
END arches.map FILE========================================
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times.
