 Galactic Amoebas

 This fractal is one I found in 2016 while experimenting with one of Jim Muth's favorite formulas, the FinDivBrot-2. The formula makes nice fractals and I was interested in seeing what it would look like when used with the parallel resistor formula that I have posted here many times before. Jim's original formula with a = -1 in simplified form is: z = b * z * z / (1 / z + b) + pixel Using it in the parallel resistor formula, rp = 1 / (1/r +1/r) I got. z1 = b * z * z / (1 / z + b) z = 1 / (1 / (z1 + c1) + 1 / (z1 + c2)) You never know if something like this will make an interesting fractal without trying it. Since I was just exploring, I used Jim's original color map. You can probably guess what happened. I found this fractal that I liked with Jim's colors. I couldn't change it without losing the nice green galactic nebula appearance. So here it is with Jim's original color map unchanged. Hal Lane and I explored many other fractals in this formula. It tends to make a lot of fractals with tendrils. A few are visible at the boundary between the green and the black along the left side in this image. The FractInt compatible PAR file for the image is: ```GalacticAmoebas { ; Exported from Fracton. reset=2004 type=formula formulafile=fracton.frm formulaname=F_20171001_1432 passes=1 float=y center-mag=-4.057989461979981/0/112104.10256781/1/\ 0/0 params=1/0/-1/0/0/333/0/0/0/0 maxiter=2000 inside=0 outside=tdis colors=000CpEAnG9mIDcLGVOJMRLOPNPMPRKRTITVFVWDXYBY\ Z9XiYXtuSloNdiIXbEPXCUYA_Z8d_6j`4pa2uaBq`Ll`Uh_ccZ\ cYbbSebNiaHlaCoa6ra1u`4p_7jZAeYE_YHVTJWOKWJLWENWAO\ W5PW1QW8UZGYaObdWfgcjjknmsrpzvryqrxmqwhqvcpu_ptVps\ RpmVmfYi_afUebOiZHlWBpS5sP5mO6gO6aN7WN8QN8KM9EM88K\ 89M9AN9BPACRADS89N66I53D408908F19K2AQ3BW4C`5Df6Ek6\ EoFKtNPzVUzbZzkczshztbzuYzvczwczzczzczzczfc7zf7zh8\ zgKzgKzfUzfczeczeczfczhcziczjwzzwzzwzzwzzwzzwzzwzz\ wzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwzzwz\ zwzwwzwwzmwzmwzgwzcwzTwzRwzPwzOwzKwzHwzEwzBwz8wzFw\ zMwzTwz_wzfwzmwztwzzwzqwzhwzZwzQwzHwbUwZewVqwMiwMd\ wN_wNWwORwONVONUONUNMUNMTNMTNMTMLSMLSMLSMLSMLSLKRL\ KRKJRKJQKJQKJQKJQKJQKJPKJPJIPJIPJIOIHOIHOIHNIHeLTh\ GNYFINEDCD81D45O89YBAcBBiBCoBDuBNg9YU7hG5s34lB6fK8\ _TATaCNiEGrGAzILlQW_XfMdeLedLecKfbKfaKf`Kf`KfAlfBk\ hCijDhlEfnFeoHcqIbsFsADqC }``` ```frm:F_20171001_1432 { ; Based on Lucid_Dreams June 10, 2016 by Jim Muth ; Modified for use in parallel resistor formula esc=(16),b=imag(p3), c1=p1+pixel,c2=p2+pixel, z=1/(1/c1+1/c2): z1=(b)*(z*z/(1/z+b)), z=1/(1/(z1+c1)+1/(z1+c2)), |z|