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(a)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=========================================
