Rosecurve

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Variations Based on the Rose Curve


The rose or rhodonea curve is shaped like a flower with petals, obtained by plotting a sine curve in polar coordinates. Its shape is determined by the frequency of the sine wave, denoted k. It is finite when k is rational, meaning it is a fraction of two integers kn/kd. The results of various combinations of numerator and denominator are shown in the chart below, created by Jason Davies. The full rose effect of non-integer values requires multiple cycles and many of the variations listed here plot only the first so won’t produce the complete curve.

https://en.wikipedia.org/wiki/Rose_(mathematics)

https://www.mathcurve.com/courbes2d.gb/rosace/rosace.shtml

epispiral

An inside-out rose curve, known as an epispiral curve.

Type: 2D half-blur
Author: cyberxaos
Date: 3 Aug 2007

Epispiral is a rose curve which is inverted on the unit circle (see spherical), so the “petals” point towards the origin and extend out to infinity. Some implementations spell the name with a capital ‘E’.

ParameterDescription
nThe frequency of the rose curve. Normally an integer; produces n inverted petals when odd, or 2n when even. Other values are allowed and produce intermediate results (but won’t produce the entire curve).
thicknessWhen non-zero, it adds thickness.
holesWhen n is even, every other petal is stretched towards the origin by this factor, touching the origin when 1, and looping to the other side when larger. The other petals are shrunk away from the origin. When n is odd, the effect is similar but the stretching and shrinking happens simultaneously to each petal.

http://www.deviantart.com/art/BD-s-2-New-Scripts-80636384

https://mathworld.wolfram.com/Epispiral.html

https://www.mathcurve.com/courbes2d.gb/epi/epi.shtml

epispiral_wf

Alternate version of epispiral.

Type: 2D half-blur
Author: Andreas Maschke (thorgor6)
Date: 12 Jun 2011

Like epispiral, but with only one variable, and the result is half the size.

ParameterDescription
wavesThe frequency of the rose curve. Normally an integer; produces this many inverted petals when odd, or twice as many when even. Other values are allowed and produce intermediate results (but won’t produce the entire curve).

flower

Filled-in rose curve; looks like a flower with petals.

Type: 2D half-blur
Author: cyberxaos
Date: Apr 2007

Originally from the Z+C++ Apophysis branch by cyberxaos, Jed Kelsey (Lu-Kout) included it in his plugin pack for users of standard Apophysis. Flower2 and Z_flower were also included in Apophysis plugin packs by Fred E (morphapoph) and Gregory Zitelli, respectively; they work exactly the same as flower.

ParameterDescription
holes1 is normal. Larger values both increase the flower size and add holes in the center. Smaller values (down to 0.5) shrink the flower size and, if petals is odd, grow new petals in the spaces between the main ones.
petalsThe frequency of the rose curve. Normally an integer; produces this many petals when odd, or twice as many when even. Other values are allowed and produce intermediate results (but won’t produce the entire curve).

https://www.deviantart.com/cothe/art/Apophysis-Z-Plugin-Pack-61192322

https://www.deviantart.com/lu-kout/art/Apophysis-Plugin-Pack-1-v0-4-59907275

https://www.deviantart.com/morphapoph/art/Apo-Anim-friendly-Plugins-178559281

flower3D

Experimental 3D version of flower.

Type: 3D half-blur
Author: Luca G (dark-beam)
Date: 10 Nov 2011

ParameterDescription
holes1 is normal. Larger values both increase the flower size and add holes in the center. Smaller values (down to 0.5) shrink the flower size and, if petals is odd, grow new petals in the spaces between the main ones.
petalsThe frequency of the rose curve. Normally an integer; produces this many petals when odd, or twice as many when even. Other values are allowed and produce intermediate results (but won’t produce the entire curve).
zpetalsThe frequency of the rose curve in the z direction.

https://www.deviantart.com/dark-beam/art/Flower3D-apoplugin-268287892

maurer_rose

String art on a rose curve.

Type: 2D half-blur
Author: Gregg Helt (cozyg)
Date: 30 Sep 2017

ParameterDescription
knRose curve numerator
kdRose curve denominator
cRose curve offset (addition to rose curve equation)
line_offset_degreesStep size from one endpoint to the next along the rose curve, in degrees. Think of driving 360 nails along the rose curve; this is the number of nails between endpoints of each Maurer line.
line_countNumber of Maurer lines to display (fewer will be visible when they overlap); increase the value if there are unwanted gaps in the result
show_linesRelative density of the Maurer lines (0 to hide them)
show_pointsRelative density of the endpoints (0 to hide them)
show_curveRelative density of the rose curve (0 to hide it)
line_thicknessThickness of the Maurer lines
point_thicknessThickness of the endpoints
curve_thicknessThickness of the rose curve

pRose3D

Rose curve with three dimensional shaping

Type: 3D half-blur
Author: Larry Berlin (aporev)
Date: 15 Oct 2009

ParameterDescription
lLength of the petals
kThe frequency of the rose curve. Normally an integer; produces this many petals when odd, or twice as many when even. Other values are allowed and produce intermediate results (but won’t produce the entire curve).
cRotation amount
z1Z scale for the main rose
z2Z scale for the reflection rose
refScReflection scale relative to the main one
opt1 for shaping option 1, 2 for option 2, or between 1 and 2 to interpolate. Or use a negative value to make a reflection.
optScOption scale factor
opt30 for option set by opt, 1 for option 3, between 0 and 1 to interpolate. Or use a negative value to make a reflection.
transpDensity of the reflection from 0 (no density) to 1 (full density)
distDistance between main and reflection
wagscWaggle scale (radial effects)
crvscCurvature scale (called srvsc in JWildfire (typo))
fFrequency of wiggle curves (circumference effects)
wigscWiggle scale (circumference effects)
offsetWiggle offset

https://www.deviantart.com/aporev/art/pRose3D-Plugin-140417044

rhodonea

Advanced rose curve

Type: 2D (can be half-blur or crop)
Author: Gregg Helt (cozyg)
Date: 24 May 2015

ParameterDescription
knumerRose curve numerator
kdenomRose curve denominator
inner_modeTransform mode when input point is on or inside the curve:
0 – Curve only
1 – Spread mode 1
2 – Spread mode 2
3 – Spread mode 3
4 – Spread mode 4
5 – Mask inside the curve
6 – Mask outside the curve
outer_modeTransform mode when input point is outside the curve (values same as inner_mode)
inner_spreadSpread amount for inner_modes 1-4
outer_spreadSpread amount for outer_modes 1-4
inner_spread_ratioThe x to y ratio for inner_spread; 1 for normal, larger to shrink x, smaller to expand x
outer_spread_ratioThe x to y ratio for outer_spread; 1 for normal, larger to expand x, smaller to shrink x
spread_splitRatio between inner and outer spread; 1 to make them equal, larger to make outer spread larger
fillAmount to thicken curve
radial_offsetRose curve offset (addition to rose curve equation)
cyclesNumber of cycles to plot: 0 to calculate automatically; set manually if needed (may be fractional, for example 0.5 for half a cycle)
cycle_offsetOffset for input points, in radians
metacyclesNumber of times to repeat the curve if cycles is 0 (calculated automatically)
metacycle_expansionAmount to expand (or contract if negative) repeated closed cycles

rose_wf

Simple rose curve.

Type: 2D half-blur
Author: Andreas Maschke (thargor6)
Date: 12 Jun 2011

ParameterDescription
ampAmplitude of the rose curve.
wavesThe frequency of the rose curve; must be an integer. Produces this many petals when odd, or twice as many when even.
filled0 for an outline, 1 for filled (like flower)

https://mathworld.wolfram.com/Rose.html

Info


This information has been created by Rick Sidwell as a guide to the more popular variations used in fractal flames. Not all of the variations are included with JWildfire, but a great many are, so it is worthwhile learning about them here.

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