HomeVariation TypesLine Shapes

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.

Download Sample flames and resources

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

ParameterDescription
offsetValue added to ρ (the distance from the origin) for each point; it expands some parts of the curve while contracting others (the points where ρ is negative)
unified_inner_outerWhether “inner” and “outer” points should be treated the same:
0: Treat inner and outer points separately
1: Treat all points as outer points (inner parameters will have no effect)
outer_modeSpread mode for outer points; 0 for no spread (outer_spread is ignored); 1, 2, 3, 4, or 5 for different spread effects
inner_modeSpread mode for inner points; 0 for no spread (inner_spread is ignored); 1, 2, 3, 4, or 5 for different spread effects
outer_spreadAmount of spread for outer points (all points if unified_inner_outer is 1)
inner_spreadAmount of spread for inner points (ignored if unified_inner_outer is 1)
outer_spread_ratioRatio of horizontal to vertical spreading for outer points; 1 to spread evenly both directions
inner_spread_ratioRatio of horizontal to vertical spreading for inner points; 1 to spread evenly both directions
spread_splitAdjusts the threshold for distinguishing outer and inner points. For some modes, it also changes the spread.
cyclesNumber of cycles to plot; 0 to calculate automatically
fillAmount of fill to add; 0 for none

Wikipedia description
Mathworld description
Description and examples by Paul Bourke

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

ParameterDescription
levelThe number of levels to draw; higher values make more complex curves
line_thicknessThickness of the lines

Wikipedia description

gosper_js

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

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

ParameterDescription
levelThe number of levels to draw; higher values make more complex curves
line_thicknessThickness of the lines

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

ParameterDescription
presetIdThe type of figure to draw; 0-9 use lines and 10-19 use circles
number_lines/circlesThe number of lines or circles to draw in the figure
filled circles1 for filled circles, 0 for outlines (only applies to figures made from circles)
a-pParameters that change the appearance of the figure, depending on the preset (not all presets use all of the parameters)

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.

ParameterDescription
seedThe seed for generating random values for the other parameters; change the seed to generate new values (but the new values, although changed, don’t appear immediately; you need to go to another transform and come back to see the new values)
timeThe amount of “time” to run the harmonograph; larger values create more loops, as if the harmonograph was run for a longer time
a1, a2, a3, a4The amplitudes for oscillators 1, 2, 3, and 4; set to 0 to disable a specific oscillator
f1, f2, f3, f4The frequencies of oscillators 1, 2, 3, and 4
p1, p2, p3, p4The phases of oscillators 1, 2, 3, and 4, in degrees
d1, d2, d3, d4The damping factors of oscillators 1, 2, 3, and 4; typically very small:
0 to disable damping
positive for normal damping (amplitude diminishes over time)
negative for reverse damping (amplitude increases over time)

Wikipedia description
Harmonographs: A Subtle Artform
Author’s description in the JWildfire forum

hilbert_js

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

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

ParameterDescription
levelThe number of levels to draw; higher values make more complex curves
show_lines1 to show the lines; 0 to hide them
line_thicknessThickness of the lines (if shown)
show_points1 to show endpoints of the lines; 0 to hide them
point_thicknessThickness of the points (if shown)

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

ParameterDescription
levelThe number of levels to draw; higher values make more intricate shapes
sizeSets the size of the H-tree
show_lines1 to show the lines; 0 to hide them
line_thicknessThickness of the lines (if shown)
show_points1 to show endpoints of the lines; 0 to hide them
point_thicknessThickness of the points (if shown)

Wikipedia description

koch_js

Draws a Koch curve.

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

ParameterDescription
levelThe number of levels to draw; higher values make more complex curves
show_lines1 to show the lines; 0 to hide them
line_thicknessThickness of the lines (if shown)
show_points1 to show points at the corners of each square; 0 to hide them
point_thicknessThickness of the points (if shown)

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.

ParameterDescription
deltaThe angle of the line in the XY plane; 0 is positive x, 0.5 is positive y (down), -0.5 is negative y (up), 1 or -1 is negative x
phiThe angle of the line in the XZ plane; 0 is positive x, 0.5 is positive z, -0.5 is negative z, 1 or -1 is negative x

lissajous

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

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

ParameterDescription
tmin, tmaxThe minimum and maximum values for the parametric equation parameter, which determines the endpoints for the curve; typically -π to +π
a, bThe frequencies of the x and y components; the shape of the curve is determined by their ratio. They are normally integers, but this is not required.
cThe amount of diagonal movement, 0 for a standard Lissajous curve; set to a small amount and increase the range of tmin to tmax to repeat the curve along the diagonal
dThe phase difference between the x and y frequencies, in radians, between -π and π; the most common values are 0 and π/2 (1.5708)
eThe thickness of the line used to draw the curve; 0 for a line

Apophysis plugin
Description at Fractal Formulas
MathWorld description
Wikipedia description
Mathcurve description

rsquares_js

Draws a pattern of recursively placed squares.

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

ParameterDescription
levelThe number of levels to draw; higher values make more complex curves
show_lines1 to show the lines; 0 to hide them
line_thicknessThickness of the lines (if shown)
show_points1 to show points at the corners of each square; 0 to hide them
point_thicknessThickness of the points (if shown)

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.

ParameterDescription
aThe radius of the fixed disk, which should be positive and relatively small (the default value of 3 is much too large); as a rule of thumb, the sum of a and b should be around 1
bThe radius of the rotating disk; make it positive for an epitrochoid (rotating around the outside of the fixed disk) or negative for a hypotrochoid (rotating around the inside). It is typically smaller than a (the default value of 2 is too large) and must not be 0.
c1, c2These are normally equal and positive, representing the distance from the center of the rotating disk where the pen is located; they may be different to achieve special effects (the default values of 0 will result in a circle)
dNormally set to 0 (the default); other values modify the figure, but not in a way that creates something new which can’t be obtained by modifying the other parameters
tmin, tmaxThe minimum and maximum values for t, the parametric equation parameter; reasonable values are 0 and 1000 (the default values of -1 and 1 do not give it enough range)
ymin, ymaxControl the line thickness; set both to 0 for a normal line, or set ymin to a very small negative value (like -0.01) and ymax to the corresponding positive value for a ribbon effect (the default values of -1 and 1 result in a very thick line)

Apophysis plugin
Description at Fractal Formulas
Wikipedia description
Spirograph Tutorial
Floral Celebration Tutorial
JWildfire Blue Stew or Julian Meets Spirograph Tutorial

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

ParameterDescription
aSize of the fixed circle
bSize of the moving circle that goes around the fixed circle; positive to go around the outside (making an epitrochoid) or negative to go around the inside (making a hypotrochoid)
cDistance from the center of the moving circle where the “pen” goes
widthPen width; keep it small (like 0.03)
modePen mode; only effect if pen width is not 0
0: ribbon
1: twisted ribbon
2: wire
3: gaussian
4: double pen (two lines width apart)
direct_color0 for normal, 1 to use direct color

tree_js

Draws a fractal tree.

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

ParameterDescription
levelThe number of levels to draw; higher values make more intricate shapes
show_lines1 to show the lines; 0 to hide them
line_thicknessThickness of the lines (if shown)
bend_angleBend angle for the tree, clockwise in degrees
branch_angleBranch angle, in degrees
branch_ratioRatio of the side branches to the main branch; 0.5 to make them equal
show_points1 to show endpoints of the lines; 0 to hide them
point_thicknessThickness of the points (if shown)

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.

ParameterDescription
weightThe extent of the arches; 2 for a full double arch; 1 gives the right half


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.
Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

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