Fractal visionaries:

I often ponder such deep questions as, "what is the best Mandelbrot set I've ever produced."  A definitive answer might not exist, but today's surprising little midget is high on the list.  I've posted it as a reward for those few who took the trouble to draw the six views of the same lost, misshapen midget that I posted yesterday.

I've always had problems with Newton's method formulas.  I just can't seem to get them right.  Today's fractal is a good example.  I was after a Newton's image; I got a Mandelbrot set instead.  But the Mandelbrot set is so unusual that I still have the formula in my permanent file.

The gravelly texture that fills the image is due to the extremely small cutoff value of |a|.  Although the color palette in the attached par file does not show it very clearly, the gravelly texture, which appears to be infinitely divisible, gives a fair appearance of a PHC image, especially when drawn at a high resolution.  Experiment with the colors a bit; you'll be surprised at the effects that are possible.

Unlike yesterday's six unfortunate images, today's image has been successfully posted to Usenet, where it hangs on a.b.p.f. and a.f.p.  I have decided not to post yesterday's images to the binaries groups.  A second look convinced me that they are not worth the bandwidth.

For tomorrow's fractal, I'll return to those weird julibrot planes I'm fascinated with.  Until then, stay cool or keep warm, depending on which hemisphere you're living in.

Jim Muth
jamth@mindspring.com


START 19.6 FILE=============================================

Gritty_Endurance   { ; time=0:00:18.00-SF5 on P4-2000
  reset=1960 type=formula formulafile=jim.frm
  formulaname=MandNewt06 passes=1 center-mag=-3.281\
  72/0/3.164669 params=8/0/5/0/1.5/0 float=y
  maxiter=200 inside=bof61 logmap=yes symmetry=xaxis
  periodicity=50
  colors=000Ur6_Y3dE0eK2fQ4fW6ga85Fd5Cg49j45m32p53j7\
  4d95_B6UD7ODERELTESWEYZEdaFkcFrfPfkZUphItr5yCARG9W\
  L8`P7eT5kX4pa3ue2zU2tI3m63g73b84Y94TB5PC5KD5FE6AF6\
  5FC8GICGOFHVJH`MHfPIlTIrWFm_Chc9bg6Yk3TonQcoCEmEHk\
  FKhHNfIQdKTbLVaJQaIM`GH`FD_D8_C4WOQT_kRWkOSkMOkKKj\
  IGjFCjD8jEEhFLfGRdIYbJc_KiYLpWMvUQuWVsZZr`bpcfoekm\
  goljsjlplnmmpjorgqtdrvatxclwedvgXuiQukItmAso2rjBbd\
  JO_S8eWIk`Spdavhk0zb9xaIv_StZ`qYioWrmVgjVXgVNeUCbU\
  1_U9WUHSUPOUWLUcHUkDUs9UqGUoMUmTTk_TieTglTerScyS9R\
  57NM5Ib3EsHPsV_tgjtuutluibtYUtN_oQfkSlfVsbXyY_sbcm\
  gfgkjapmWuqRkkN`eIRZEGT96NC6OF6PH7RK7SN7TJDQEINAOJ\
  5TG1ZD6VLBRTHN`MJgRFoWBwXDqXGkYIeYL_ZNUdQXiU`oXct`\
  gzcjt_gmXegTbaQ`VMYPIVIFTCBQFJSHQVKYXMdZPlaRscXgkb\
  XrhLzeRXbX4a`E`eOZiYYmg_kaajXchRefLgeGicAjfEkhIkkM\
  lnQmpUnsYnuaoxe`jULWI6I66MA6QD5UH5YK5`O5dR4hV4lYDd\
  XNXWWQVeIUnATjJOfSKa`FYiA }

frm:MandNewt06 {; Jim Muth
z=c=(pixel*p1):
a=z^3+(c-p2)*z-c
b=p3*z^2+c-1
z=z-1*a/b
.000000000000000000000000000001 <= |a| }

END 19.6 FILE===============================================