FOTD -- January 11, 2002 (Rating 5) Fractal visionaries and enthusiasts: Today's image is a picture of a quadratic Mandelbrot midget. But it does not look like a Mandelbrot midget. It looks like a fragment of a horizontal slit. It looks like a horizontal slit because that's what it is. Mandelbrot midgets are actually holes in the four-dimensional Julibrot figure, sliced in a particular direction. The holes are nowhere near hyperspherical. They are flat spaces with two extended dimensions (in the Z plane) and two contracted dimen- sions (in the C plane). These flat spaces are not unbroken, but are largely filled-in with low-iteration features. They are like places where midgets are possible if the low-iteration stuff can only be held at bay. Since the holes are actually four-dimensional, they can be sliced in many directions. When they are sliced in the contracted Mandelbrot or extended Julia directions, the slice is a nice small Mandelbrot midget or much larger mini-Julia set that fits nicely on the screen. But when the holes are sliced in odd directions, as is the case in today's image, the slice will contain both extended and contracted features, and will usually appear stretched, requiring anti-stretching and skewing to counter the distortion. In today's image, the stretching and skewing are only moderate, but some odd-angle images must be stretched by a factor in the thousands. More on the Julibrot and fourth dimension in general in upcoming FOTD's. I named today's image "Julibrot Monster" because of its vague resemblance to a monster's face. I rated it at a 5. The 9-minute render time is a bit slow, but the finished image may be downloaded from: <http://home.att.net/~Paul.N.Lee/FotD/FotD.html> or from: <http://sdboyd.dyndns.org/~sdboyd/fotd/index.html> The lack of sun Thursday here at Fractal central made the temperature of 57F 14C feel colder than it actually was, and prevented the fractal cats from fully enjoying their afternoon romp in the yard. But it was still the best day they have had in more than a week, which made them very enjoyable cats. It's now time for the real work to get started here at F.C. Until next FOTD, take care, and don't get mired in a state of fractal indeterminacy. Jim Muth jamth@mindspring.com START 20.0 PAR-FORMULA FILE================================ Julibrot_Monster { ; time=0:09:17.61--SF5 on a P200 reset=2002 type=formula formulafile=allinone.frm formulaname=multirot-XZ-YW-new passes=1 center-mag=+0.00000000128389097/-0.000000000542546\ 13/1.435616e+008/0.9341/-179.455993649140652/-68.7\ 194309865828359 params=158/-62/2/0/-1.120224512675\ 5/-0.2638790266846/-1.1202245126755/-0.26387902668\ 46 float=y maxiter=12000 inside=0 logmap=911 colors=000UlUUmUUmUUnUUnUUoUUoUUpUUpUUqUUqUUrUUrUU\ sVUsWQtXNuZJv`EvaGvbHvcIvdJudKueLtfMtgNsgPrhQriRqj\ SqjTpkUplVomUooWomXnkYmjZlh_kf`jeahcbfacd`dbZf`Xg_\ WkYUjYUhXTfWTdVTcUTaUT_TTYSTXRTVQTTQTRPSQOSONSMMSK\ MSJKRHIQFGPDEOBCNCAMDALDAKEAKEAKFAKGAKGAKHAKHAKIAK\ IAKJAKKAKKAKLALLAKMAKN9JN9JO8IO8IP7HN2IP7HQCHRGHSL\ GTQGUUGVZGWcFXgFYlFZpFYnGXmHWlIWkJVjKUiLUgMTfMSeNS\ dORcPQbQQ`RP_SOZSOYTNXUMWVMUWLTXKSYKRYJQZIP_HO`HMa\ GLbFKcFJdEIdDHeDFfCEgBDhBCiABj9Aj98k87l76m75n64o53\ p52p75n97mB9kDCjFEhGGgIIeKLdMNcOPaQR`RUZTWYVYWX_VZ\ bU`dSafRchPekOgmMioLisLjqKkpKlnJmmJnkInjIohHpgHqeG\ rdGrbFsaFt_EuZEvXDvWDwUCxTCyRBzQBzPByOCxODwOEwOFvO\ GuOHuOItOKsOMsOOrOQqNSqNUpNWoNYoN_nN`mOamPblQckRdk\ SejTfiUghVhhWigXjfYkfZle_md`ndaocbpbcqbcracs`ct`cu\ _cvZcwZcwYcwXcwXcwVcwUcwTcwScwRcwQcwOcwNcwMcwLcwKc\ wKcwKcwKcwKcwKcwKcwKcwKcw } frm:multirot-XZ-YW-new {; Jim Muth ; 0,0=para, 90,0=obl, 0,90=elip, 90,90=rect e=exp(flip(real(p1*.01745329251994))), f=exp(flip(imag(p1*.01745329251994))), z=f*real(pixel)+p3, c=e*imag(pixel)+p4: z=z^(p2)+c, |z| <= 36 } END 20.0 PAR-FORMULA FILE==================================