# Rosecurve

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’.

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.

## 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.

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

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

## pRose3D

Rose curve with three dimensional shaping

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

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

## rhodonea

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

## rose_wf

Simple rose curve.

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

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

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