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Fractal of the Day
by Jim Muth
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Fractal visionaries and enthusiasts: Seahorse Valley never looked like this before. The unexpected shape inspired the name "Is This Seahorse Valley?" But the image most certainly is one of Seahorse Valley. The scene is an oblique view of the valley, rotated 13 degrees from the Julia orientation toward the Rectangular orientation. If anyone doubts this, change real(p1) to 90 and watch the Seahorse Valley Julia set appear. And while you're at it, change poth parts of (p1) to zero and watch Seahorse Valley itself appear at the center of the screen, awkwardly rotated 90 degrees. With all these unfamiliar aspects, what shape then is the entire Seahorse Valley area of the Julibrot? It is a tapering four-dimensional wedge that terminates in a sharp plane. A sharp plane would describe the razor edge that a 4-D man would use to shave his chin, just as a 3-D man uses a blade with a sharp line as the cutting edge. Yes, I know it's silly to think that a plane could be sharp, but the fourth dimension makes many impossible things possible. A sharp plane could extend indefinitely in all directions, yet a 4-D man could cut himself seriously if he carelessly touched it. Thank goodness we can see our fractals only two dimensions at a time. The included parameter file of today's image runs in a little over 1-1/2 minutes. The image is also conveniently available for download on the FOTD web site at: I'll probably post a few more unexpected aspects of Seahorse Valley before moving on to East Valley, which, if anything, is even more varied than Seahorse Valley. The weather turned quite pleasant here at New Fractal Central on Monday, with warm sun and a temperature of 73F 23C. The fractal cats enjoyed the fine weather as they sat on their scratching posts, soaking up the sun. My day was reasonably quiet, but that big job is still looming for later this week. The job will not arrive tomorrow however, so expect the next FOTD to be posted on schedule in 24 hours. Until then, take care, and a four dimensional man would probably cut himself in half if he stepped on one of our sidewalks. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START PARAMETER FILE=======================================
IsThisSeahrsValley { ; time=0:01:39.03--SF5 on a P200
reset=2004 type=formula formulafile=allinone.frm
formulaname=multirot-XY-ZW-new function=flip/ident
passes=1 center-mag=0/0/1.127829/1/-90/-1.2337e-014
params=77/90/2/0/0/0/-0.75/0 float=y maxiter=50000
inside=255 logmap=yes periodicity=10
colors=000E2hC2iA2p82o62n40m50l60k70j70i80h90gA0fA\
0eB0cC0aD0_D0XE0UF0RF5OCAKAEH7HL5KQ2LV0MZ4PZ8SZCUZ\
GXZJ_ZMYZOWZQU_SS_UQ_WO`YM`_K`aIacGaeEagCbiAbk8cm6\
co4bq4aq4`p4_p4Yp4Xp4Wp4Vo4Uo4To4Ro4Qn4Pn4On4Nn4Mn\
4Km4Jm4Im4Hm4Go2Em4Fl6Fj7Gi9GgAGfCHdDHcFHaGI`IIZJI\
YLJWMJVOJTPKSRKQTKPULNWLMXLKZMJ_MHaMGbNEdNDeNBgOAh\
O8jO7kP5mP2qR4nP5kO7hM8eL9bJB`ICYGDVFFSDGPCINAJNFK\
NKMNPNNUPNUONUOOUPOZROcTOhVOmTOgROaPOWNOQLSJJWDH_7\
Eb0Gc1Ic2Jc2Ld3Md3Od4Pd5Re5Se6Ue6Vf7Xf8Yf8_f9`g9bg\
AcgBehBfhChhCihDkiEliEniFoiFnjEnkEnkEmlDmlDmmDmnDl\
nCloCloCkpBkqBkqBkrBjrAjsAjtAit9iu9ju9kv9kw8mx8oy8\
rz7sz8uz8uz8sz8qz9nz9lz9jy9ix9hwAfvAfuAftAftBftBft\
BesBesBesCerCerCdrCdqDdqDdqDdpDcpDcpEcoEcoEeoEgoFi\
oEkoEmoEooDqoDsoDuoCwoCxoCzoCzoBzoBzoBzoAzoAzoAzo9\
zo9zo9zo9zo8zo8zo8zo7zo7zo7zz7zz8zz9zzAzzBzzCzzDzz\
EzzFzzGzzHzzzzzzzzzzzzzzz }
frm:multirot-XY-ZW-new {; draws 6 planes and rotations
;when fn1-2=i,f, then p1 0,0=M, 0,90=O, 90,0=E, 90,90=J
;when fn1-2=f,i, then p1 0,0=M, 0,90=R, 90,0=P, 90,90=J
a=real(p1)*.01745329251994, b=imag(p1)*.01745329251994,
z=sin(b)*fn1(real(pixel))+sin(a)*fn2(imag(pixel))+p3,
c=cos(b)*real(pixel)+cos(a)*flip(imag(pixel))+p4:
z=z^(p2)+c,
|z| <= 36 }
END PARAMETER FILE=========================================
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times.
