FOTD -- February 20, 2004 (Rating 6) Fractal visionaries and enthusiasts: Last evening I got into a discussion with the fractal lady, who is of the opinion that I am spending too much time concerning myself with such useless things as fractals and fantasies of the fourth dimension. She seemed to think that this is something only little boys do before they grow up and learn to think like sensible, practical men. When such discussions arise, I totally agree with her opinion, leaving nothing to disagree about, but to myself I often wonder how useless the fourth dimension actually is. One thing the fourth dimension most definitely is good for is fun. And if Einstein had thought it childish to consider the fourth dimension, what kind of world would we live in today? Perhaps we would not have developed computers and discovered fractals, and today's image would not exist. Today's scene reminds me of a lake with reflections shimmering off the wave tops, but it is actually a view of Seahorse Valley sliced in an unimaginable direction. These reflections needed no special formula to bring them to life. They are an actual part of the Julibrot itself. Perhaps this area should be known as "Seahorse Lake", which is the name I gave the image. Due to time limitations, I am unable to write a description of the orientation of today's image, but I will go into the curiosities of four-dimensional geometry in future FOTD's. For now, enjoy the image. It is a very fast one. I have rated today's image at a 6, which combines with the render time of just over one minute to give an overall value of 508. The image may also be viewed by going to Paul's FOTD web site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> A very pleasant and sunny late-winter day with a high temperature of 56F 13C here at Fractal Central on Thursday gave the intrepid cats a long, pleasant afternoon in the yard. When evening came, they settled down without complaint. The best news is that today looks to be a repeat. For me, the work is rather heavy, but it is under control, and will be finished in plenty time for another trip to the fourth dimension to find another fractal. The fractal I find will appear as tomorrow's FOTD. Until then, take care, and the everyday world we live in is four-dimensional, so what's the fuss about? Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ Seahorse_Lake { ; time=0:01:11.01--SF5 on a P200 reset=2003 type=formula formulafile=allinone.frm formulaname=SliceJulibrot2 passes=1 periodicity=10 center-mag=-0.0812181/5.55112e-016/3.045118/0.62/9\ 0/3.885780586188e-016 params=45/90/0/90/-0.75/0/0/0 float=y maxiter=50000 inside=0 logmap=yes colors=000dAjcAibAhaAg`Af_AeZAdYAcXAbWAaVA`UA_TAZS\ AYRAXQ9WP9VO9TN9SM9QL9OK9MJ9KH9IB9GA9EMMMQQQSUUX__\ beelpouyxntvgot`jsVeqO`oHWnARl4Nk5Pj6Qi7Rh7Tg8Ug9V\ fAWeAYdBZdC_cC`bDbaEc`Fd`Ff_GgZHhYIiYIkXJlWKmVKnVH\ gNEeFBc7Ca8D_8EY9FW9GU9GUAHUAIUBJUBKUBKUCLUCMUCNUD\ OUDOUEPUEQUERUFSUFSUFTXHTZJU`LUbMVdOVfQWhSWjTXlVXn\ XXpYTqWPoVLmUHkTDiSCgQBeOBcNAaLA_K9YI9WH8UF8WEAYGC\ ZHE_JG`KIaLKbNLcONdPPeRRfSTgUVhVWiWYjY_kZal_cmaenb\ focdqaer`gsZitYkuWmvVowUquSstRurQwqPzoNwnMumLskKqj\ IohHmgGkfFidDgcCeaBc`Aa_9_`CY`EW`GUaJSaLSaNTbQVbSW\ bUXbWYcVZdU_dT`eSafSbfRcgQdhPehPfiOfiNgjMhkLikLjlK\ kmJlmImnInoHooGppFppFnqImqKlrNjrPisRhsUftWetYdu`cu\ bavd`vg_wiYwkXxnWxpVxrWvqXtqYrqZpq_nq`lqajpbhpcfpd\ dpebpe`pfZogXohVoiTojRokPolNnmLnnJnoHnpFnpEnmDlkDk\ iDjgDieDhcDgaDf_DeYDdAKUWDcq7pp6lp6ho5eo5ao4Yn4VZT\ c_Re`QfaOgbMhcLidJjeIlfGm } frm:SliceJulibrot2 {; draws most slices of Julibrot pix=pixel, u=real(pix), v=imag(pix), a=pi*real(p1*0.0055555555555556), b=pi*imag(p1*0.0055555555555556), g=pi*real(p2*0.0055555555555556), d=pi*imag(p2*0.0055555555555556), ca=cos(a), cb=cos(b), sb=sin(b), cg=cos(g), sg=sin(g), cd=cos(d), sd=sin(d), p=u*cg*cd-v*(ca*sb*sg*cd+ca*cb*sd), q=u*cg*sd+v*(ca*cb*cd-ca*sb*sg*sd), r=u*sg+v*ca*sb*cg, s=v*sin(a), c=p+flip(q)+p3, z=r+flip(s)+p4: z=sqr(z)+c |z|<=9 } END 20.0 PAR-FORMULA FILE==================================