FOTD -- January 19, 2003 (Rating 5) Fractal visionaries and enthusiasts: Since yesterday's FOTD I have continued to work with a variation of the Tman formula that was posted on Friday. Working with this formula gives the impression that more than three dimen- sions are involved. I can get no clear mental image of slicing through a single 3-D object. And if there is only one dimension in addition to the two on the screen, why are the two variable parameters needed to fully explore it?. Morgan has also commen- ted on this, but for now, we'll assume that we're dealing with a three-dimensional M-set (and a six-dimensional Julibrot?). Today's image lies in the default fractal created by the TMan1 variation, near the point at the northern edge, where the two straight stretched arms criss-cross. I named the image "Maximum Spirals". I have rarely seen an image with so many spirals surrounding a midget. In the parent fractal, the scene is stretched, (foreshortened actually), and skewed. So in order to have a normal image I needed to unstretch and unskew the scene. When this was done, I was left with an image that rates a 5. I could rate the image no higher than a 5 because it duplicates scenes that lie in spirals in many valleys of the classic M-set. I don't expect to find any totally new Mandelbrot features in this formula or its variations. The interest lies in discover- ing which parts of the classic M-set are reflected in which parts of the new-shaped Mandelbrot fractals. I'll continue working with these fractals of ambiguous dimension for a few days, then it will be back to the ever-fruitful M-Mix4 formula. The render time of 9 minutes can be avoided by downloading the GIF image from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The weather was sunny but very cold and breezy all day here at Fractal Central. The temperature in the teens F, around -9C, kept the dynamic cats glued to the warmest spots they could find. They moved around enough to ask for food and eat, but retired as soon as their meal was done. It's cold again this morning, with clouds and a few flakes of snow in the air. But it is not as cold as yesterday. Only time will tell if the snow will turn heavier and if the intrepid cats will venture outdoors. I find myself with nothing to do again today. If I play my cards right, I'll get through the entire day without doing anything that can be considered work. Until next FOTD, take care, and one must work hard to be truly lazy. Jim Muth jamth@mindspring.com jimmuth@aol.com START 20.0 PAR-FORMULA FILE================================ Maximum_Spirals { ; time=0:09:08.43--SF5 on a P200 reset=2002 type=formula formulafile=triter.frm formulaname=TMan1 passes=1 center-mag=-0.003218524\ 4524517/+0.7498998373975185/2.623604e+007/4.125/-4\ 6.9647077347951267/-9.94802466789319162 params=0/0 float=y maxiter=4200 inside=0 periodicity=0 colors=000kRElLInRFoXDqaBrg8tm6tt1ur4uq6up9uoBunDu\ mGulIukLujNuiPuhSvgUvfXveZvd`vccvbevahv`jv_lvZovYq\ vXsuWruWquWpuVouVnuVmuUluUkuUjtTitThtTgtSftSetSdtR\ ctRbtRasQasQ`sQ_sPZsPYsPXsOWsOVsOUrNTrNSrNRrMQrMPr\ MOrLNrLMrLLvJJrLLoNMkOOhQPeRRaTSZVUVWVSYXOYXPZYQZZ\ QZZRZ_SZ_SZ`TZaUZaU_bV_bW_cW_dX_dY_eY_eZ_fZ_f_`g_`\ g_ah`ah`ai`bi`biacjacjackbdkbdkbdlbelcemcfmcfmdfnd\ gndgodgoehoehpeipfiqfiqfjqfkrgkrgksglshlshlthlvhlu\ ikwikuikvjkxjkyjkwjjwijuhjsgjsfiqehodgmcflbejadi`c\ g_afZ`dY_bXZaWY_VWZUVXTUWTTUSSTRRRQPQPOOONNNMLMLJL\ JIKIGJHFIGDHFCGDAFC9EB7DA6C94B71C83D95EA7FA9GBBHCD\ IDFJDGKEILFKMGMNGOOHQPISQJUQJVRKXSLZTM`UMbVNdWOfXP\ hYPiZQk_Rm`SoaSqbTscUudVwcWwdVxdVxeVxeVxeUyfUyfUyg\ UygTzgTzhTzhTzhTziUwiVuiWsiXqiYojZmjZkj_ij`gjaekbc\ kcakc_kdYkeWlfUlgSlhQlhOliMmjKmkImlGmmEnoBmmCmlClk\ CljCkiCkhCjgDjfDidDicDhbD } frm:TMan1 { c1=flip(real(pixel)),c2=imag(pixel),c3=p1 z1=z2=z3=0: t1=z1*z1+2*z2*z3 t2=z3*z3+2*z1*z2 t3=z2*z2+2*z3*z1 z1=t1+c1,z2=t2-c2*c2,z3=t3+c3 z=z1+z2+z3 |z| < 8 } END 20.0 PAR-FORMULA FILE==================================