FOTD -- September 24, 2009 (Rating 9) Fractal visionaries and enthusiasts: A FOTD fractal with a rating of a 9 is a rare beast, but today we have one, a welcome relief from the string of 6 and 7 rated images. The parent fractal came about when I subtracted 0.2 part of Z^(-7) from 0.2 part of Z^3 and added (1/C). This parent resembles nothing as much as a network looking like an overdone pancake with various shaped holes scattered about. The largest hole is a twisted Mandelbrot set with a wedge pointed at its East Valley. Today's scene is located on the shoreline of this wedge. The unusual effect was achieved by rendering the scene with both the outside and inside set to 'fmod' with a proximity of 1. The image is divided about 50-50 between inside and outside parts. One glance at the image will show why I rated it at a 9. A second glance will explain the name "Bubbles in the Blue". The calculation time of just over 1 minute will make taking the glances a very brief task. But there are always those overquali- fied computers that will not run DOS fractint. Those with such units may view the finished image on the FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> My Wednesday ponderings were on the four-dimensional phenomenon known as double rotation, where an object such as a hypersphere may be subject to two totally independent and distinct rotations at the same time. Of all the unvisualizable things possible in 4-D space, this is perhaps the most intriguing, for unlike most other 4-D stuff, it has no analog in 3-D space. Morning sun gave way to afternoon clouds here at Fractal Central on Wednesday, while the temperature reached a summer-like 82F 28C. The fractal cats are still more concerned with their power- ful new catnip rats than the weather. My day was about average. The next FOTD will be posted in 24 hours. Until then, take care, and what we need is a fractal tea party. Jim Muth jamth@mindspring.com jimmuth@aol.com START PARAMETER FILE======================================= Bubbles_in_theBlue { ; time=0:01:07.12-SF5 on P4-2000 reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=recip passes=1 center-mag=+1.110714075944/+0.083632827962/4955856\ /1/87.5/0 params=-0.2/-7/0.2/3/0/0/0/0 float=y maxiter=500 inside=fmod proximity=1 outside=fmod logmap=yes periodicity=10 colors=000zzzvyvrxrmwmhvmcumZtmUsmPrmKqmFpmAom6nm6\ mm6mm6mm6lm6lm6km6km6jm6jm6im6im6hm6hm6gm6gm6gm6fm\ 6fm6fm6fm6em6em6em6em6dm6dm6dm6dm6cm6cm6cm6cm5bm5b\ m5bm5bm5am5am5am5`m5`m5`m5`m5_m5_m5_m5_m5Zm5Zm5Zm5\ Zl5Yk5Yj5Yi5Yh5Xh5Xh5Xh5Wh5Wh5Wg5Wf5Ve5Vd5Vc5Vb5Ua\ 5U`5U_5UZ4TZ4TZ4TZ4TZ4SZ4SZ4SZ4SZ4RZ4RZ4RZ4QZ4QZ4Q\ Z4QZ4PZ4PZ4PZ4PZ4OZ4OY4OY4OY4NY4NY4NY4NY4MY4MW4MW4\ LW4LV4LU4LU4KT4KT4KS4KR3JR3JR3JP3JO3IN3IM3IL3IK3HI\ 3HG3HE3HC3GB3GA3GA3FA3FA3FA3FA3EA3EA4EA6EA8DBADCCD\ DEDEGEFIEFKEFMEFOFFQFFSFFUFFWFFYFF_FP`FPaFPbFPcFPd\ FPeFPfFPgFPhFPiFPjFPkFPlFPmFPmCQnEPnFPnGPnHPoJOoKO\ oLOoMOpNOpPNpQNpRNqSNqUMqVMqWMrXMrYMr_Lr`LsaLsbLsd\ KseKtfKtgKthKtjJukJulJumJupIvsIvvIzzmzzzzzmvvItrIs\ oIrmIpkIoiImgIlfIkdIibIh`IgZIeXIdVIbTIaRI`QIZOIYMI\ WKIVIIUGISEIRCIQBISCHTDGUDGWEFXFFYFE_GE`HDaHCcICdJ\ BpKMnKNmJOlJPjIQiIRgHSfHT } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================