|
Fractal of the Day
by Jim Muth
|
|
Fractal visionaries and enthusiasts: A formula that draws the 3-D triternion Mandelbrot set was posted yesterday to the Fractint list by Russell Walsmith. As posted, the formula draws slices in the XY orientation of the 3-D M-set. After seeing what the formula would do, and being unable to resist experimentation, I made a slight modification to it. I flipped the value of initial c1 from real to imaginary, and named the modified formula TMan1. The change enables the formula to draw what I assume is the YZ orientation. Of course, it could be the XZ orientation, or something in between. I have no idea how triternions work. But regardless of the orientation, the revised formula draws slices with intact midgets. Many of these midgets duplicate scenes in the classic M-set, but some midgets are entirely different, doing strange things even while we watch. Today's image illustrates one of these new and unusual midgets. The midget (or half-midget) appears to be rising above a horizon that consists of part of another, larger midget. The fragment of a larger midget is stretched, most likely because the larger midget lies in a different plane. In the 2-D M-set, midgets are oriented in every possible direction. I assume the same thing happens with an even greater degree of freedom in the 3-D M-set. Overlapping features such as those pictured in today's scene are common in the hypercomplex M-set, but I have never seen both stretched and unstretched Mandelbrot features overlapping. I need to do much more experimenting with this three-dimensional Mandelbrot set. For now however, I'll settle for a FOTD image that rates a 6. The rating reflects the mathematical worth of the image. The artistic worth barely rates a 4. The name "Rising Mandelbrot" was inspired by the impression of one Mandelbrot midget rising above the horizon-like edge of another. The render time of 10 minutes can be avoided by downloading the completed GIF image from: The fractal weather was cold here at Fractal Central on Friday. With a temperature of 25F -4C, brisk winds, and occasional showers of snow waiting for them, the cats didn't even think of going out. They were quite contented lying by their radiators. Today is even colder, (the 8am temperature was 7F -14C), so they will be housebound for at least another day. As for me, I've got a bit of work to wrap up, then a day with little to do but wander through FractalLand. If I find anything worthwhile, it will appear as tomorrow's FOTD. Until then, take care, and when the going gets tough, get a fractal going. Jim Muth jamth@mindspring.com jimmuth@aol.com |
START 20.0 PAR-FORMULA FILE================================
Rising_Mandelbrot { ; time=0:10:14.45--SF5 on a P200
reset=2002 type=formula formulafile=triter.frm
formulaname=TMan1 center-mag=-0.33019260452431920/\
+0.53369254258170410/2256.431/3.3373/149.75/-15.93\
32167459564502 params=-0.4/0 float=y maxiter=18000
inside=0 logmap=94 periodicity=10
colors=000UKATKASKARKAQKAPKAOKANKAMKBLJCKKDJKEIKGH\
KHGLIFLKELLDLNCMODMPDMREMSFNUGNVHNWINYJOZKO`LOaMOb\
NPdNPeOPgPPhQQiRQkSQlTQnURoVRpWRrXRsXRtWSsWSsWSsWT\
sWTsWTsWTsWUsVUsVUsVVsVVsVVsVVsVWsVWsUWsUWsUXsUXsU\
XrUYrUYrUYrTYrTZrTZrTZrTZrT_rT_rT_rS`rS`rS`rS`rSar\
SarSarVbvTatSarR`pQ`nP_lO_jN_hMZfLZdKYbJY`IYZHXXGX\
VFWUEWSDVQCVOBVMAUK9UI8TG7TE6TC5SA4S83R62R41R33Q55\
Q77P89PAAOBCODENFGNGHMIJMJLLLNLMOLOQKQSKRUJTWJUXIW\
ZIX`HZbH`cGaeGcgFdiFflDhjFgiGfhHegIdfJcdKbcLabM`aO\
_`PZZQYYRXXSXWTWVUVTVUSWTRYSQZRP_QN`PMaOLbNKcMJdLH\
dKIeLIeLJeLJeMKeMKfMKfMLfNLfNMfNMfNMgONgONgOOgPOgP\
OhPPhPPhQQhQQhQUfPQhQNiRJjRGkSCmT9nT2oU4qS6pT8pUAp\
VCpVEpWGpXIpYKp_MpaOpcQpeSpgUpiWpjYpk_plapmcpnepog\
pphpqiprjpskptlpumpvmpwmpxmpympzmpzmpzmpzmpzmpzmpz\
mpzmpzmpzmozmozmozmozmozmozmnzmnzmnzmnzmnzmnzmmzmm\
zmmzmmzmmzmmzmlzmlzmlzmlz }
frm:TMan1 {
c1=flip(real(pixel)),c2=imag(pixel),c3=p1
z1=z2=z3=0:
t1=z1*z1+2*z2*z3
t2=z3*z3+2*z1*z2
t3=z2*z2+2*z3*z1
z1=t1+c1,z2=t2-c2*c2,z3=t3+c3
z=z1+z2+z3
|z| < 8 }
END 20.0 PAR-FORMULA FILE==================================
|
times.
