# Line Shapes

Shape variations made from lines. Like all shape variations, they ignore the input. Some are generated using parametric equations. Others use algorithmic techniques.

## arch

A double arch.

Type: 2D blur
Author: Antonio Intrieri (gygrazok)
Date: 9 Feb 2007

The variation amount controls the extent of the arches. Use 2 for a full double arch; 1 gives the right half.

## butterfly_fay

A butterfly shaped curve discovered by Temple H Fay in 1989.

Type: 2D blur
Author: Gregg Helt (cozyg)
Date: 24 May 2015

## chrysanthemum

Chrysanthemum flower shaped curve.

Type: 2D blur
Author: Jesus Sosa
Date: 1 Feb 2018

Description and examples by Paul Bourke

## dragon_js

Draws a Heighway dragon curve.

Type: 2D blur
Author: Jesus Sosa
Date: 17 Oct 2017

Wikipedia description

## gosper_js

Draws a Gosper island curve, also known as a flowsnake.

Type: 2D blur
Author: Jesus Sosa
Date: 17 Oct 2017

Wolfram MathWorld description

## hamid_js

Figures made from lines and circles based on works by Iranian mathematician Hamid Naderi Yeganeh.

Type: 2D blur
Author: Jesus Sosa
Date: 29 Mar 2018

Mathematical Concepts Illustrated by Hamid Naderi Yeganeh

## harmonograph_js

Figures that might be made from a swinging pendulum on a harmonograph.

Type: 2D blur
Author: Jesus Sosa
Date: 8 Dec 2018

There are many types of harmonograph devices. This variation uses four independent oscillators: 1 and 2 control x; 3 and 4 control y.

## hilbert_js

Draws a Hilbert curve, a fractal space-filling curve.

Type: 2D blur
Author: Jesus Sosa
Date: 21 Dec 2017

Wikipedia description

## htree_js

Draws an H-tree (made from lines in the shape of the letter H).

Type: 2D blur
Author: Jesus Sosa
Date: 17 Oct 2017

Wikipedia description

## koch_js

Draws a Koch curve.

Type: 2D blur
Author: Jesus Sosa
Date: 17 Oct 2017

Larry Riddle’s Koch Curve page

## line

A straight line.

Type: 3D blur
Author: Nic Anderson (chronologicaldot)
Date: 5 Mar 2014

A line that starts at the origin with a length specified by the variation amount. The direction is determined by the parameters.

## lissajous

A Lissajous curve (named for Jules-Antoine Lissajous, who studied them).

Type: 2D blur
Author: Jed Kelsey (Lu-Kout)
Date: 16 Jul 2007

## rsquares_js

Draws a pattern of recursively placed squares.

Type: 2D blur
Author: Jesus Sosa
Date: 17 Oct 2017

## spirograph

A Spirograph figure (epitrochoid or hypotrochoid).

Type: 2D blur
Author: Jed Kelsey (Lu-Kout)
Date: 16 Jul 2007

The Spirograph toy has a plastic gear with multiple holes for a pen that is rotated around either the outside of another fixed disc or the inside of a fixed ring. Mathematically, the figures are called, respectively, epitrochoids or hypotrochoids.

There is also a different Apophysis plugin named spirograph, but it doesn’t seem to work correctly (I think the formulas get sin and cos confused).

## spirograph3D

A 3D Spirograph figure.

Type: 3D blur
Author: Rick Sidwell
Date: 19 Jun 2017

## tree_js

Draws a fractal tree.

Type: 2D blur
Author: Jesus Sosa
Date: 17 Oct 2017

## Z_arch

A double arch.

Type: 2D blur
Author: Antonio Intrieri (gygrazok) and Gregory Zitelli (cothe)
Date: 1 Aug 2007

Z_arch is just like arch, except that it uses a parameter to control the arch extant instead of the variation amount.

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.