FOTD -- April 24, 2002 (Rating 8) Fractal visionaries and enthusiasts: Today's fractal is a picture of a midget in the Z^sqrt(3)+C fractal, a fractal that is infinite both in surface extent and in its depth. The particular midget in today's image is located in a cut-off fragment of a spiral elephant-trunk located in the East Valley area of the parent fractal, which is shaped surprisingly like the classic M-set. This midget is one of the more interesting ones I have found in the range between the linear non-fractal Z+C and the ultimate fractal Z^2+C. The MandelbrotBC1 formula is a great help in getting the most out of fractals in this range. If the image on one level of the logarithmic spiral shows little of interest, I merely go up to the next level by adjusting the real(p2) parameter. I named the image "Scherzo", a word that describes a lively and humorous musical composition. It was the first word that came to mind, and has little to do with the actual appearance of the fractal. Because it is perhaps the most satisfactory midget I have yet found in these under Z^2 fractals, I rated it a lofty 8, a rating that might be a bit liberal. An extra feature of the image is that it renders from the parameter file in under 5 minutes. But 5 minutes can seem an awfully long time when one is waiting for a fractal to finish and other things need to be done. Relief for impatience is at hand in the form of the completed GIF image, which is available on the W.W.Web at Paul's site at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at Scott's site at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The fractal weather Tuesday here at Fractal Central was brisk and breezy, with a temperature of 55F 13C. But a strong sun peeking between the clouds gave enough warmth on the porch to keep the fractal cats happy for over an hour. My happiness did not arrive until I had most of the day's work behind me. And then I was happy. I'll be even happier when today's work is behind me. But the greatest happiness of all will come when the FOTD CD is finished and if it proves to be a success. I'm currently involved in re-writing many of the short stories I have written over the past 20 years. When reading my own writing some 10 to 20 years after I wrote it, I sometimes wonder how I could have written something so trite, and then there are the all-too-few times when I wonder how I could have written something so good. Regardless, the next ongoing FOTD will appear on April 27th. Until then, take care, and hold your breath. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Scherzo { ; time=0:04:43.20--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=recip passes=1 center-mag=-0.21378685445671390/-0.076303594971113\ 36/337296.3/1/-162.5/-1.8837750803690767e-010 params=1.73205/0/30.69/0 float=y maxiter=1800 inside=0 logmap=130 symmetry=none periodicity=10 colors=000L00P30S60V70_A0aD0dF0gG3jGCmILpISrI`uJix\ JpzLyzLzzLzxazpszizzdzz`zzXzzUzzOymJxcFuZAsW6rJ1oM\ 0mP0lS0jT1c`DYfPQm`LslDzx7zz1zy1yo1ld1`X1OM1CC1031\ 0970FC9LILQMVXSfaUpfUzcUpZUgUUaPUWKTQFSKASE0QQ0QQ0\ QQ0PQ0PP0PP0OP0OP0OO0MO0MO0MO0LM0LM0LM0LM9WgCeuYTi\ TKmO7p03z9FzOPzc_zrizofzldzjazg`zfYzcXz`Tz_SzXPzVO\ z_SxaXud`ridolijomgsrdvvayz_ssVomSjgPfaMaXJYQGSJDO\ DAJ77F14A01600400400400300300300100100100000000000\ 00000000000000000000000000000000000000000000000000\ 0000000000000000000000000000000000000TzDSyCSxCSxCQ\ vCQvAQuAPsAPsAPrAOr9Op9Op9Mo9Mm9Mm7Ll7Ll9LjAJjCJiD\ JgFIgGIfIIfJGdLGdMGcOFaPFaQF`SD`TD_VDYXCYYCX_CX`AV\ aCVcETdHSfJSgMQiOQjRPlTPmVOoWMpYMrZLs_Lu`JvaJxbIyc\ GzdGzeFzfFzgDzhDziCzjAzkAzl9zn9zp7zq6zr6zt4zz4zz3z\ z3zz1zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0zz0\ zz0zz0zz0zz0zz0zz0zz0zz0z } frm:MandelbrotBC1 { ; by several Fractint users e=p1, a=imag(p2)+100 p=real(p2)+PI q=2*PI*fn1(p/(2*PI)) r=real(p2)-q Z=C=Pixel: Z=log(Z) IF(imag(Z)>r) Z=Z+flip(2*PI) ENDIF Z=exp(e*(Z+flip(q)))+C |Z|<a } END 20.0 PAR-FORMULA FILE==================================