Fractal visionaries and enthusiasts: 

Today's striking image combines four parts of straight Z with three parts of Z^2, two parts of Z^3 and only one part of Z^4 on each iteration before adding straight C.  This whimsical assemblage of numbers creates a parent fractal that is basically a classic Mandelbrot set.  This M-set however is surrounded by a vast cloud of satellite dots, each of which is an entire fractal universe.  Today's scene is located in one of these island universes in the interior of the north branch of Seahorse Valley of the parent M-set.

The terraced effect was created by rendering the image with the outside set to 'tdis', which measures the total distance a point travels before it escapes over the fractal horizon.

The critical point of today's concoction was rather easy to find.  When the first rough approximation registered -0.9998..., it was a pretty sure sign that the exact critical point is likely minus-1, a common critical point.  When I entered this value, it proved to be correct.

The art and math values both rate an 8, at least in my opinion.  The rather slow calculation time of 3-1/2 minutes is a drawback however, though the web sites can take care of this time problem.

A cloudless sky and a temperature of 66F 19C made today near perfect for the end of summer here at Fractal Central.  The fractal cat must have thought so as he sat on his scratching post and pondered the pigeons feeding in the back yard.  The humans spent the day wondering what is wrong with the world.

The next FOTD will be posted in the right divine time.  Until the deity speaks, take care, and when a man kills 12 people with a gun, blame the gun, then try to get the politicians to pass legislation that would reduce the number of mass shootings.  (I'll have much more to say about such simple minded thinking in a day or two.)

Jim (neither on the right nor the left) Muth
jimmuth@earthlink.net


START PARAMETER FILE=======================================

Seahorse_Symphony  { ; time=0:03:30.00 SF5 at 2000MHZ
  reset=2004 type=formula formulafile=basicer.frm
  formulaname=MandelbrotMix3a function=ident passes=1
  center-mag=+0.7859446718496711/+0.0203918179218428\
  /3.352754e+009/1/-75/0 params=4/1/3/2/2/3/1/4/-1/0
  float=y maxiter=900 inside=0 outside=tdis
  periodicity=6 mathtolerance=0.05/1
  colors=000OzaMzcLx`JrYJlXIdTG_SGTPFMOFGLDAJC3GC0FA\
  0CA0AC06D33FA0GJ0IS0I_0FV0DS0AP19M46J74GA1DD0AG07J\
  04M01P00L00G00C00700G91PS7XjDdzjfzrzzdlfLrP0K90K4K\
  l0Ug0ac0f_0jV0oXFrYTu_gy`vzazzazsdzifyYguOipCjm1lj\
  IdiY_fmTdzOTpgIdzaMpv4gz0_6zzCxvIrjOlYSfM`cXgado`m\
  v_voVyiQzcMzXIzQDzL9zF6zLCzQIzXMzOIzFFz4Az07z04z03\
  zMdMG`OCXP6SQ0OS0JTFCQY4Op0Lz0JrYPczTVzQOvOFoL7gI0\
  `F0TD0XL0_S1`_4cf7dmIjdSoXauOjyFuz6zz0zz0yV1l0DjD7\
  jd1oi4rl7uoAyrDzuGzxJzzMupGggAVY4IP04G0GIPQIrXMjaP\
  dgT_lXTr_OxcIzfCzi6SzaTzTVzMVzFGzL1zP_r09fA4_G0SM0\
  LS0DY06a04c03d43dA1fG0gL0gX4Xf9MrDAzI0pMAdQLTVVJ_d\
  7co0gy0jz9QlV6Qp06OJX0ou0im0df0__0VS0QL0LD0G60C04F\
  6OICfLJxMPyOOzPLzQJzQGzSFzTCzVAzV9z_AscCjgDclFVpFM\
  uGFyI6zJJQfPQdVQa`Q_fQXjQVdSY`S`XScSSdOSgJSjFSlJTa\
  MTTPTJSTAVT1TMFSGQQ9cP3oO0zM0zI4zFJzII0JP0LX0Mc1Mj\
  6OrAPyFPzI_zPgzXpzagz_`pX }

frm:MandelbrotMix3a {; Jim Muth
z=real(p5), c=fn1(pixel), a=real(p1), b=imag(p1),
d=real(p2), f=imag(p2), g=real(p3), h=imag(p3),
j=real(p4), k=imag(p4), l=imag(p5)+100:
z=(a*(z^b))+(d*(z^f))+(g*(z^h))+(j*(z^k))+c,
|z| <=l }




END PARAMETER FILE=========================================