At 03:51 PM 10/31/11 -0600, Mike wrote:
....Anyone that has taken electrical engineering is familiar with the formula for parallel resistance:
rp = 1 / ( 1 / r1 + 1 / r2 )
If you put a mandelbrot equation at r1 and r2 with a different center point you have it....
Mike: Very good idea -- parallel resistance. Electricity and fractals. I guess it's all one grand unified universe, based on numbers. What your formula creates appears to be fractals of the type created by combining positive and negative exponents of Z, such as the one created by the parameter file at the end of this letter. Increase the value of real(p2) and the Mandies shrink; decrease the value and they expand and merge, as they are starting to do in the image drawn by the included file. I also see fractals drawn by your formula that resemble those created by my DivideBrot series of formulas, with debris filling the usually empty insides. But your formula gives control over the position of the Mandies that I cannot achieve with my formulas. I'll have more to say later. Jim Muth jamth@mindspring.com START PARAMETER FILE======================================= Multi_Mandies { ; time=0:00:23.29 SF5 at 200MHZ reset=2004 type=formula formulafile=basicer.frm formulaname=MandAutoCritInZ function=ident inside=0 center-mag=-0.414649/-0.442222/0.9690955/1/-35/0 params=1/2/-0.025/-2/0/0/0/0 float=y maxiter=1500 colors=00000e0e00eee00e0eeL0eeeLLLLLzLzLLzzzLLzLzz\ zLzzz000555888BBBEEEHHHKKKOOOSSSWWW___ccchhhmmmsss\ zzz00zG0zV0zj0zz0zz0jz0Vz0Gz00zG0zV0zj0zz0jz0Vz0Gz\ 00z00zG0zV0zj0zz0jz0Vz0GzVVzbVzjVzrVzzVzzVrzVjzVbz\ VVzbVzjVzrVzzVrzVjzVbzVVzVVzbVzjVzrVzzVrzVjzVbzhhz\ lhzqhzuhzzhzzhuzhqzhlzhhzlhzqhzuhzzhuzhqzhlzhhzhhz\ lhzqhzuhzzhuzhqzhlz00S70SE0SL0SS0SS0LS0ES07S00S70S\ E0SL0SS0LS0ES07S00S00S70SE0SL0SS0LS0ES07SEESHESLES\ OESSESSEOSELSEHSEESHESLESOESSEOSELSEHSEESEESHESLES\ OESSEOSELSEHSKKSMKSOKSQKSSKSSKQSKOSKMSKKSMKSOKSQKS\ SKQSKOSKMSKKSKKSMKSOKSQKSSKQSKOSKMS00G40G80GC0GG0G\ G0CG08G04G00G40G80GC0GG0CG08G04G00G00G40G80GC0GG0C\ G08G04G88GA8GC8GE8GG8GG8EG8CG8AG88GA8GC8GE8GG8EG8C\ G8AG88G88GA8GC8GE8GG8EG8CG8AGBBGCBGDBGFBGGBGGBFGBD\ GBCGBBGCBGDBGFBGGBFGBDGBCGBBGBBGCBGDBGFBGGBFGBDGBC\ G000000000000000000000000 } frm:MandAutoCritInZ {; Jim Muth a=real(p1), b=imag(p1), d=real(p2), f=imag(p2), g=1/f, h=1/d, j=1/(f-b), z=(((-a*b*g*h)^j)+(p4)), k=real(p3)+1, l=imag(p3)+100, c=fn1(pixel): z=k*((a*(z^b))+(d*(z^f)))+c, |z| < l } END PARAMETER FILE=========================================