Rose Range Lite

Coloring Formula

by Kerry Mitchell, 14 Feb 2000

Basic information

A "rose curve" is one given in polar coordinates:
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.

Parameters

Hints

Since the ribbons of color can be very thin, use either "multipass linear" or "one pass linear" as the calculation mode.

Very powerful images can be made by having a totally black gradient (eliminate all the control points), and setting the solid color to white.

Sample images

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
}