Fractal of the Day
by Jim Muth
FOTD -- December 21, 1998
Fractal visionaries:
Today was a fine example of a winter solstice day here at fractal central. The temperature of 55F 13C was perfect for fractal hunting among other activities. Accordingly, I hunted.
My rather hasty search of the Z^6+C Julibrot was rewarded by today's picture. This picture is a close-up of a midget in the area just beyond the last bud on the negative X-axis of the Z^6 Mandeloid. Just as in the Z^2 Mandeloid, this area is a rather difficult one, filled with feathery high-iteration features that are slow to compute.
However, today's picture, which holds the calculation time to under one hour, is not a Mandeloid. It is a slice in a remote and unnamed direction of the Julibrot. I know that it's awkward, but I just can't seem to confine myself to one or two orientations.
The scene is one of verdant growth, perhaps of strange fern-like life forms growing in the methane swamps of some far distant planet. The bright blue diagonal stripe is what I sometimes call the lane of potentiality. Potential midgets can be found only in line with this stripe or others like it.
The actual midget, which in the Mandelbrot direction appears as a five-lobed figure, is the open area at the exact center of the picture. The star-studded filaments, which are so symmetrical in the M-direction, here twist and stretch into fantastic shapes beyond description.
The whole scene reminds me of a garden in a tropical rain forest, which is why I named it "My Fractal Garden". The finished GIF file has been posted to:alt.binaries.pictures.fractalsand to:http://home.att.net/~Paul.N.Lee/FotD/FotD.html
Now it's time for me to check to see how Dr. J is making out. While I'm checking, take care, and be at peace with your fractals, even when they don't turn out the way you had hoped.
Jim Muth
jamth@mindspring.com
START FORMULA=============================================
multirot06-XZ-YW {; Jim Muth
; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect
e=exp(flip(real(p1*.01745329251994))),
f=exp(flip(imag(p1*.01745329251994))),
z=f*real(pixel)+p2, c=e*imag(pixel)+p3:
z=sqr(z)*sqr(sqr(z))+c,
|z| <= 36 }
END FORMULA===============================================
START PARAMETER FILE======================================
My_Fractal_Garden { ; 35min on a 486-100mhz, 640x480
reset=1960 type=formula formulafile=multmult.frm
formulaname=multirot06-XZ-YW passes=t
center-mag=0/0/1.892844e+008/0.5224/-57.065/64.385
params=62/22/-1.109763050693/0/-1.109763050693/0
float=y maxiter=36000 bailout=25 inside=255 logmap=400
symmetry=none periodicity=10
colors=000NAA<11>NAANAENAF<9>NAGNAGNAINAJ<29>NAKNAKNAJ\
<4>NAINAINAG<7>NAENAENAC<7>NAANAANA8<2>NA7NA7N87N77O75\
O55O45O44O24O04Q02O04O24O24N44N54N54M74M84M84MA5KA5KB5\
KC5JC5JE5JE5IE5IE5IE7IF7GF7<3>FH7FI7EJ5FK7FK7GK7GL7IL7\
<3>KM7KM7MN7<4>OR8OS8QT8QU8RU8RU8SW8<2>TX8TX8UXAUYAWYA\
<5>Z_AZ_A_aA_aAZbB_aA_aAaaAaaAaaFbaJbaNc_Rc_Uc_Y<6>fZu\
<4>hYuhYujYu<16>pWupWuqUuqUuqUusUu<2>sUusTuuTu<5>wSuwS\
z<5>zRzzRzzRzzRzzRz<6>zQzzQzzOzzQz<9>zUzcmz
}
END PARAMETER FILE========================================
START 19.6 PARAMETER-FORMULA FILE=========================
My_Fractal_Garden { ; 35min on a 486-100mhz, 640x480
reset=1960 type=formula formulafile=multmult.frm
formulaname=multirot06-XZ-YW passes=t
center-mag=0/0/1.892844e+008/0.5224/-57.065/64.385
params=62/22/-1.109763050693/0/-1.109763050693/0
float=y maxiter=36000 bailout=25 inside=255 logmap=400
symmetry=none periodicity=10
colors=000NAA<11>NAANAENAF<9>NAGNAGNAINAJ<29>NAKNAKNAJ\
<4>NAINAINAG<7>NAENAENAC<7>NAANAANA8<2>NA7NA7N87N77O75\
O55O45O44O24O04Q02O04O24O24N44N54N54M74M84M84MA5KA5KB5\
KC5JC5JE5JE5IE5IE5IE7IF7GF7<3>FH7FI7EJ5FK7FK7GK7GL7IL7\
<3>KM7KM7MN7<4>OR8OS8QT8QU8RU8RU8SW8<2>TX8TX8UXAUYAWYA\
<5>Z_AZ_A_aA_aAZbB_aA_aAaaAaaAaaFbaJbaNc_Rc_Uc_Y<6>fZu\
<4>hYuhYujYu<16>pWupWuqUuqUuqUusUu<2>sUusTuuTu<5>wSuwS\
z<5>zRzzRzzRzzRzzRz<6>zQzzQzzOzzQz<9>zUzcmz
}
frm:multirot06-XZ-YW {; Jim Muth
; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect
e=exp(flip(real(p1*.01745329251994))),
f=exp(flip(imag(p1*.01745329251994))),
z=f*real(pixel)+p2, c=e*imag(pixel)+p3:
z=sqr(z)*sqr(sqr(z))+c,
|z| <= 36 }
END 19.6 PARAMETER-FORMULA FILE===========================
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