r = a1cos(b1t) + a2sin(b2t)where "r" is the radial distance and "t" is the polar angle. It's called a rose curve because it is a series of loops, loosely resembling a rose. The number of loops, or petals, is determined by b1 and b2.
This formula colors the pixel according to how the orbit relates to a rose curve. Specifically, if the orbit ever falls into a range around the curve. This has the effect of coloring the image with a series of looping curves. The r given above is based on the angle of the iterate at each step, and becomes the center of the range. So if a particular z value has its magnitude within a certain interval around r, it is considered in the range.
Very powerful images can be made by having a totally black gradient (eliminate all the control points), and setting the solid color to white.
rose-range-lite1 { ; copyright Kerry Mitchell 14feb00
fractal:
title="Rose Range Lite 1" width=640 height=480 author="Kerry
Mitchell"
created="February 14, 2000" numlayers=2
layer:
method=multipass caption="New Layer 2" opacity=100 visible=yes
alpha=no
mergemode=multiply
mapping:
center=-0.7/0.84 magn=4.5 angle=62
formula:
filename="Standard.ufm" entry="Julia" maxiter=100 percheck=off
p_seed=0.407/0.47 p_power=2/0 p_bailout=4
inside:
transfer=none repeat=yes
outside:
filename="lkm.ucl" entry="rose-range-lite" density=4 transfer=linear
repeat=yes p_scale=1 p_rangewidth=0.25 p_colorby="last angle"
p_ac=1
p_bc=0 p_as=0.25 p_bs=4 p_curvecenter=0/0 p_rot=45
gradient:
smooth=yes numnodes=8 index=0 color=0 index=50 color=1081408
index=100
color=4240512 index=150 color=9428415 index=200 color=16777215
index=250
color=9428415 index=300 color=4240512 index=350 color=1081408
layer:
method=multipass caption="New Layer 1" visible=yes alpha=no
mapping:
center=-0.7/0.84 magn=4.5 angle=62
formula:
filename="Standard.ufm" entry="Julia" maxiter=100 percheck=off
p_seed=0.407/0.47 p_power=2/0 p_bailout=4
inside:
transfer=none repeat=yes
outside:
filename="lkm.ucl" entry="rose-range-lite" transfer=linear
repeat=yes
p_scale=1 p_rangewidth=0.25 p_colorby="last magnitude" p_ac=1
p_bc=0
p_as=0.25 p_bs=4 p_curvecenter=0/0 p_rot=45
gradient:
smooth=yes numnodes=8 index=0 color=0 index=50 color=1081408
index=100
color=4240512 index=150 color=9428415 index=200 color=16777215
index=250
color=9428415 index=300 color=4240512 index=350 color=1081408
}
rose-range-lite2 { ; copyright Kerry Mitchell 14feb00
fractal:
title="Rose Range Lite 2" width=600 height=400 author="Kerry
Mitchell"
created="February 14, 2000" numlayers=1
layer:
insolid=16777215 outsolid=16777215 method=multipass caption="Layer
1"
visible=yes alpha=no
mapping:
center=-0.0281514646853937725/0.96264291150886823 magn=15.7736999842263
angle=335.193169601693856
formula:
filename="Standard.ufm" entry="Julia" maxiter=81 percheck=off
p_seed=-0.122561166876653619/0.744861766619744237 p_power=2/0
p_bailout=4
inside:
filename="lkm.ucl" entry="rose-range-lite" transfer=linear
repeat=yes
p_scale=1 p_rangewidth=0.111111111111111111 p_colorby="first
magnitude"
p_ac=1 p_bc=3 p_as=0 p_bs=0 p_curvecenter=0/0 p_rot=-33
outside:
filename="lkm.ucl" entry="rose-range-lite" transfer=linear
repeat=yes
p_scale=1 p_rangewidth=0.111111111111111111 p_colorby="first
magnitude"
p_ac=1 p_bc=3 p_as=0 p_bs=0 p_curvecenter=0/0 p_rot=-33
gradient:
smooth=yes numnodes=4 index=0 color=16777215 index=100 color=8355711
index=200 color=0 index=300 color=8355711
}