FOTD -- February 09, 2003 (Rating 5) Fractal visionaries and enthusiasts: Today's fractal is named "Irregular Minibrot". The reason for the name is the shape of the midget and the irregularity of the features around it. The midget is irregular because instead of iterating Z^2, I iterated Z^sqrt(2) and chose a spot 14.142 levels down the logarithmic spiral to do the rendering. When this low a power of Z is iterated to make a fractal, the results are totally unpredictable. Mandeloids generally have a number of lobes one less than the exponent of Z in the generating expression. Thus the formula Z^5+C draws a Mandeloid with 4 lobes, and the Z^2+C Mandeloid, which is the classic Mandelbrot set, has one lobe. Following this progression, the Z^1.4142 Mandeloid has only 0.4142 lobe, less than half a lobe, but there is no easy rule determining which fraction of a single lobe will appear either in the parent fractal or in the midgets it contains. Theoretically, today's midget is only less than half there. Its buds are smaller than those of the classic M-set and more widely spaced. In addition, the buds are in the wrong places and mis- shapen as well. There are several smaller midgets in the image, which are easily found by toggling into and out of color mode. Some of these may also be interesting. I have not checked to see. With all its imperfections, today's FOTD makes an interesting image, though not interesting enough to rise above the rating of an average 5 that I gave it. The render time of 7 minutes is fair enough for such a mediocre image, and most of that time can be saved by downloading the fully-rendered GIF image from one of the FOTD web sites at: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> and at: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather remained sunny all day Saturday here at Fractal Central, but the temperature of 25F -4C proved far too extreme for the whiskers of the cats, who poked their noses out the door only long enough to sample the chill and determine that they did not want to be outside. Today is starting warmer, but it is cloudy, so the effect on the dynamic duo will likely be the same. I have nothing much planned for the day, other than exploring Fractal Land that is, so I'll take it an hour at a time. Until next FOTD, take care, and can the shape of fractals be influenced by the power of thought? Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ Irregular_Minibrot { ; time=0:07:26:88--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=MandelbrotBC1 function=floor passes=1 center-mag=+0.86416652796344500/+0.512463707154294\ 50/1904.762/1/67.5/-5.01217123360930827e-012 params=1.4142/0/-14.142/0 float=y maxiter=6000 inside=0 logmap=73 periodicity=10 colors=000SZSQYROXQMWPKVOIUNFTMCSL9RK6QJ3PH4OI4NI4\ MI5LI5KJ5JJ5IJ6HJ6GK6FK7FK7EK7DL7CL8BL8AL89M98M97M\ 96M72L84M96MA8NBANCCOCEODGPEIPFKQGMQHORHQRISSJUSKW\ TMYTOYTQXVSXWUWXWWXYVY_VZaU_cU_eT_gT_iS_kR_mQ_oP_m\ OYkNXiMWfLVdKUbJU`ITYHTWGSUFSSESPDRNCRLBQIAQG9PE8P\ C8O97O77N57N37N49N5AN5CN6DN7EN7GN8HN9IN9KNALNBMNBO\ NCPN5PQCQNIULPXJV`GacEggCmjAnhBngCofDoeEpdFpcGqbHq\ aIr`JsYGrZIr_Jr`KraLqbMqcOqdPqeQpfRpgSphTpiVpjWokX\ olYomZon`noanpbnqcnrdpxcnselnfkjhieig`jfXldSmbOscO\ pcOndOldOidOgeOeeOceO`fOZfOXgOVgOSgOQhOOhOMhOJiOHi\ OFoIAiODdTF_ZIVcKQiNLnPGsRKnQOjRSeSV_TZXUbWVfUWeWX\ eYYd_Zda_cc`ceabhbbkcandaqe`tfdwgbzh`ziZzjXzkVzlTz\ mRznPzoNzpLzqJzrHzsFztDzuBzv6zwAzxEzyIzzMzzQzzUzzX\ zz`zzdzzhzzlzzpzztzzxzzwzzwzzwzzwzzwzzwzzyzzwzzuzz\ szzqzzozzmzzkzzizzgzzezzczzazz_zzYzzWzzUzzSzzQzzOz\ zMzzKzzIzzJzzHzzGzzFzzDzz } 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==================================