zn = zn-1 * zn-1 + c,
the previous 2 values of z are used:
zn = zn-1 * zn-2 + c.
This is similar to the Fibonaccisequence, wherein each subsequent number is the sum of the previous 2:
Fn = Fn-1 + Fn-2.
The standard Fibonacci sequence isinitialized with 1, 1, and the Fibonacci Mandelbrot formula initializes2 z variables to the same value before beginning iterating. Fromthere, the new z is found from the product of the previous 2, and the previousz values are updated. The Julia variation works similarly, initializingboth z variables to the pixel value. The "switch" feature togglesfrom Mandelbrot to Julia formula, and back.
fibonacci-mandelbrot { ; copyright Kerry Mitchell 06dec2000
fractal:
title="Fibonacci Mandelbrot" width=640 height=480 author="Kerry Mitchell"
created="December 6, 2000" numlayers=1
layer:
method=multipass caption="Layer 1" visible=yes alpha=no
mapping:
center=-0.196016295020040017/0.988335576644839503
magn=51.8280916861211811 angle=346.607221186724228
formula:
filename="lkm.ufm" entry="fibonacci-mandelbrot" maxiter=1000
percheck=off p_initialz=0/0 p_bailout=1000 p_order="2" p_weight1=1/0
p_weight2=1/0 p_weight3=1/0 p_weight4=1/0
inside:
transfer=none repeat=yes
outside:
transfer=linear repeat=yes
gradient:
smooth=yes numnodes=9 index=33 color=127 index=83 color=16638 index=133
color=65535 index=134 color=327679 index=183 color=12582910 index=228
color=16711551 index=283 color=16695296 index=333 color=16646144
index=383 color=4128768
}
fibonacci-julia { ; copyright Kerry Mitchell 06dec2000
fractal:
title="Fibonacci Julia" width=480 height=480 author="Kerry Mitchell"
created="December 6, 2000" numlayers=1
layer:
caption="Layer 1" visible=yes alpha=no
mapping:
center=-0.12/0 magn=1.75 angle=270
formula:
filename="lkm.ufm" entry="fibonacci-julia" maxiter=1000 percheck=off
p_julparam=0.494204037933724129/0.0472742539328047258 p_bailout=1000
p_order="3" p_weight1=1/0 p_weight2=1/0 p_weight3=1/0 p_weight4=1/0
inside:
transfer=none repeat=yes
outside:
filename="dmj.ucl" entry="dmj-Smooth" transfer=sqrt repeat=yes
p_power=1.9/0 p_bailout=1000000
gradient:
smooth=yes numnodes=8 index=14 color=11796660 index=64 color=14319578
index=114 color=16777215 index=164 color=8355839 index=214 color=255
index=264 color=127 index=314 color=0 index=364 color=5898330
}