HomeVariation InformationVariation List

Variation List

Flame Fractal Variations – Rick Sidwell

This is an attempt to list summary information and resources about the many variations used in programs like Apophysis and JWildfire. Right now, it is more an experiment. With a thousand variations to cover, it will take awhile to get them all! Most variations are grouped with similar ones, so scroll up or down when you get to a variation summary to see them. There are two ways to browse the information:

  • By variation name. Start this page, which lists the variations in alphabetical order with a one line description of each. Click on the variation you want information on.
  • By group. Start at Groups, which list the grouping of variations with images representing the variations in each group. Click on the group name to see the group or on an image to go to the specific variation it exemplifies.

I personally use JWildfire most often for generating fractal flames, and have used it to create most of the example images. However, this project is not limited to that program, and includes variations made for other programs as well. However, with very few exceptions, only variations for which source code is available are listed here. If you find errors, feel free to create an issue by scrolling to the top of any page and clicking “Issues”. But please don’t create issues for missing variations; I’m already aware most variations are missing.

Variations and their Types

TypesVariationDescription
Line ShapesarchA double arch.
WavesaugerWave effect that gets stronger further from the origin
Linearbi_linearSwap x and y
BlobsblobPushes and pulls the plane using a radial sine wave to make it look like a blob.
Blobsblob_fl“Fluid” version of blob; allows fractional values for waves
Blobsblob2Modulate a flame using radial sine waves.
Blobsblob3DA variant of blob that adds a 3D component.
ShapesblurCircle with a bright centre.
Shapesblur_circleCircle with even coloring.
Shapesblur_heartCreates a heart from two ellipses.
Blurryblur_linearCreate a motion blur effect.
Blurryblur_pixelizeAverages colors in an area to make large square pixels.
Blurryblur_zoomCreate a zoom blur effect.
Shapesblur3DThree dimensional Gaussian blur.
BoardersboardersDivide the plane into squares with borders.
Boardersboarders2Divide the plane into squares with borders, with parameters.
ReshapersbutterflyReshape squares centered at the origin into butterfly shapes.
Line Shapesbutterfly_fayA butterfly shaped curve discovered by Temple H Fay in 1989.
Polar Shapescannabiscurve_wfShape resembling a cannabis leaf.
Patternscheckerboard_wfGenerate a checkerboard pattern.
ShredderschecksDivides the flame into a checkerboard and shifts half of the squares up and left and the other half down and right.
ShapeschrysanthemumChrysanthemum flower shaped curve.
Polar Shapescloverleaf_wfShape resembling a four leaf clover.
ShapescircleblurCircle with even coloring.
ReshaperscirclizeReshape squares centered at the origin into circles.
Reshaperscirclize2Reshape squares centered at the origin into circles (scaled to work better with other variations)
Shape GroupscircleRandRandom size circles in a grid.
SplitterscirclesplitSplit the flame in a circle centered at the origin.
SplitterscircusScale the unit circle and the the rest of the flame separately.
Attractorsclifford_jsStrange attractor attributed to Cliff Pickover
Importerscolormap_wf /
post_colormap_wf
Load colors from an external image.
Polar Shapesconic/conic2Conic section shape (ellipse, parabola, or hyperbola)
SplitterscornersSplits the plane along the x and y axes and stretches it as if tugging the corners.
CpowcpowRaise input point to a complex power specified by its real and imaginary parts
Cpowcpow2Raise input point to a complex power specified in polar coordinates
Cpowcpow3Raise input point to a complex power to produce a spiral
Cpowcpow3_wfAttempt to port cpow2 to JWildfire that  "by happy accident became something else"
Lineardc_linearDirect color version of linear3D.
Inversiond_sphericalCombines spherical and linear
DiscdiscSwap polar coordinates ρ and θ.
Discdisc2Swap polar coordinates ρ and θ, but using Manhattan distance instead of
Euclidean.
Discdisc3Swap polar coordinates ρ and θ, with parameters.
Discdisc3dSwap 2D polar coordinates ρ and θ and transforms z according to the distance from the origin.
Stamps outline: 0px;text-underline-position: under" rel="noopener">dc_acrilicCreate a pattern reminiscent of acrylic pour painting.
Stamps outline: 0px;text-underline-position: under" rel="noopener">dc_apollonianCreate a colorful pattern.
Boardersdc_boardersPresumably, a direct color version of boarders, but it appears to be the same as boarders.
Stamps text-underline-position: under" rel="noopener">dc_booleansCreates patterns based on boolean operators.
Stamps transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s;
text-underline-position: under" rel="noopener">dc_butterflies
Creates butterfly patterns using a Nova fractal
Stamps text-underline-position: under" rel="noopener">dc_cairotilesCreate patterns from rotated squares in a grid.
Stamps transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s;
outline: 0px;text-underline-position: under" rel="noopener">dc_circlesblue
Create random bubbles.
Stamps outline: 0px;text-underline-position: under" rel="noopener">dc_circuitsCreate a pattern reminiscent of a circuit board.
Stamps text-underline-position: under" rel="noopener">dc_codeCreate a fractal picture, using arbitrary code.
Stamps text-underline-position: under" rel="noopener">dc_ducksCreate a fractal "ducks" pattern.
Stamps transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s;
text-underline-position: under" rel="noopener">dc_fingerprint
Create a pattern resembling a fingerprint.
Stamps transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s;
text-underline-position: under" rel="noopener">dc_fractaldots
Create a pattern from fractally arranged dots.
Stampsdc_gabornoiseGenerate a pattern resembling Gabor noise.
Stampsdc_glyphoGenerate a pattern based on rings of nested circles.
Stampsdc_grid3DGenerate a 2D image of a 3D grid.
Stampsdc_hexagonsGenerate a hexagon grid pattern.
Stamps text-underline-position: under" rel="noopener">dc_hoshiCreate a design based on fractal hoshi tiling.
Stamps transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s;
text-underline-position: under" rel="noopener">dc_hyperbolictile
Create a {3,8} hyperbolic tessellation mapped to a Poincare disk.
Stampsdc_inversionCreate a fractal design based on circle inversion.
Stamps transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s" rel="noopener">dc_kaleidocomplexGenerate a kaleidoscopic pattern.
Stamps transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s" rel="noopener">dc_kaleidoscopicGenerate a kaleidoscopic pattern.
Stamps outline: 0px;text-underline-position: under" rel="noopener">dc_kalisetGenerate a pattern using Kalisets.
Stampsdc_kaliset2Generate a pattern using kalisets.
Stamps text-underline-position: under" rel="noopener">dc_layersCreate a layered pattern of wavy circles.
Stamps outline: 0px;text-underline-position: under" rel="noopener">dc_mandalaCreate a kaleidoscopic mandala pattern.
Stamps text-underline-position: under" rel="noopener">dc_mandbrotCreate a kaleidoscopic pattern based on the Mandelbrot set.
Stamps transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s" rel="noopener">dc_mandelbox2DCreate a two dimensional Mandelbox pattern.
Stampsdc_mengerGenerate a Sierpiński carpet pattern (looks like the face of a Menger sponge).
Stampsdc_moebiuslogCreate a spiraling pattern using log and a Möbius transform.
Stamps text-underline-position: under" rel="noopener">dc_pentatilesGenerate a pattern of tiled pentagons.
Stamps transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s" rel="noopener">dc_poincarediscGenerate a hyperbolic tiling mapped to a Poincare disk.
Stamps text-underline-position: under" rel="noopener">dc_quadtreeCreate a graphical display of a random quadtree.
Stamps transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s" rel="noopener">dc_randomoctreeCreate a graphical (2D) display of a random (3D) octree.
Stamps outline: 0px;text-underline-position: under" rel="noopener">dc_rotationsCreate a pattern using repeated rotations.
Stampsdc_spacefoldCreate a pattern using a space folding technique.
Stampsdc_squaresCreate a pattern of squares on a grid.
Stamps text-underline-position: under" rel="noopener">dc_starsfieldCreate a field of stars.
Stampsdc_sunflowerCreate a pattern of spirals.
Stampsdc_teslaCreate a pattern resembling electrical arcing.
Stampsdc_treeGenerate a tree shape.
Stamps text-underline-position: under" rel="noopener">dc_triantessConstruct a tiling using Wythoff construction.
Stamps text-underline-position: under" rel="noopener">dc_truchetGenerate a truchet tiling pattern.
Stamps text-underline-position: under" rel="noopener">dc_turbulenceGenerate a turbulence noise pattern.
Stampsdc_voronoiseGenerate a pattern based on a combination of Voronoi diagrams and noise.
Stampsdc_vortexCreate a pattern from a train of vortices.
Stampsdc_warpingGenerate a texture using fBm warping.
Stamps text-underline-position: under" rel="noopener">dc_worley
Linear text-underline-position: under" rel="noopener">dc_linearDirect color version of linear3D
Patternsdc_perlinGenerate a pattern based on fractal Brownian motion (fBm), also known as Perlin noise.
Patternsdla_wfCreate a simple Diffusion Limited Aggregation (DLA) pattern.
Patternsdla3d_wfCreate a 3D Diffusion Limited Aggregation (DLA) mesh.
Line Shapesdragon_jsDraws a Heighway dragon curve.
CpowdrosteImplements Eschers map using logarithms; same effect as escher
DiscediscSwap elliptic coordinates μ and ν.
JuliaeJuliaPolynomial Julia sets in elliptic coordinates
RosecurveepispiralAn inside-out rose curve, known as an epispiral curve
Rosecurveepispiral_wfAlternate version of epispiral
CpowescherImplements Escher’s Map
BlurryexblurBlur effect radiating from a point
Z ManipulationextrudeExtrude the other variations on the transform by stretching the z coordinate
FlippersfanDivides the plane into pie shaped wedges and rotates them (dependent variation).
Flippersfan2Divides the plane into pie shaped wedges and rotates them.
DiscfdiscSwap polar coordinates ρ and θ, first taking the reciprocal of ρ; scales
by 2𝜋 instead of 𝜋.
Z ManipulationflattenFlatten the flame by setting the z coordinate to 0
FlippersflipcircleFlips the points inside a circle centred at the origin top to bottom.
FlippersflipyFlips the points on the right side of the y-axis top to bottom.
RosecurveflowerFilled-in rose curve; looks like a flower with petals
Blobsflower_dbReshape a flame into a 3D flower
Rosecurveflower3DExperimental 3D version of flower
Shapesgaussian_blurFuzzy circle with a bright center, made from a Gaussian distribution
Attractorsgingerbread_manAn attractor that resembles a gingerbread man
Flippersglitchy1Mix of  (divide flame into strips and flip them) and  (blur to resemble flowing pixels).
Stamps outline: 0px;text-underline-position: under" rel="noopener">glsl_acrilicCreate a pattern reminiscent of acrylic pour painting.
Stamps transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s;
text-underline-position: under" rel="noopener">glsl_apollonian
Create a colorful pattern.
Stamps transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s" rel="noopener">glsl_circlesblueCreate random bubbles.
Stamps text-underline-position: under" rel="noopener">glsl_circuitsCreate a pattern reminiscent of a circuit board.
Stamps text-underline-position: under" rel="noopener">glsl_codeCreate a fractal picture, using arbitrary code.
Stamps transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s" rel="noopener">glsl_fractaldotsCreate a pattern from fractally arranged dots.
Stampsglsl_grid3DGenerate a 2D image of a 3D grid.
Stampsglsl_hoshiCreate a design based on fractal hoshi tiling.
Stamps transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s;
text-underline-position: under" rel="noopener">glsl_hyperbolictile
Create a {3,8} hyperbolic tessellation mapped to a Poincaré disk.
Stamps transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s" rel="noopener">glsl_kaleidocomplexGenerate a kaleidoscopic pattern.
Stamps transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s" rel="noopener">glsl_kaleidoscopicGenerate a kaleidoscopic pattern.
Stampsglsl_kalisetGenerate a pattern using Kalisets.
Stamps text-underline-position: under" rel="noopener">glsl_kaliset2Generate a pattern using Kalisets.
Stampsglsl_mandalaCreate a kaleidoscopic mandala pattern.
Stamps transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s" rel="noopener">glsl_mandelbox2DCreate a two dimensional Mandelbox pattern.
Stamps transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s" rel="noopener">glsl_randomoctreeCreate a graphical (2D) display of a random (3D) octree
Stamps outline: 0px;text-underline-position: under" rel="noopener">glsl_squaresCreate a pattern of squares on a grid.
Stamps transition: color 0.1s ease-in-out 0s, background-color 0.1s ease-in-out 0s" rel="noopener">glsl_starsfieldCreate a field of stars.
Line Shapesgosper_jsDraws a Gosper island curve, also known as a flowsnake.
Shape GroupsgpatternA grid pattern of polygons.
Attractorsgumowski_miraThe strange attractor of Gumowski-Mira
Line Shapeshamid_jsFigures made from lines and circles based on works by Iranian mathematician Hamid Naderi
Yeganeh.
Line Shapesharmonograph_jsFigures that might be made from a swinging pendulum on a harmonograph.
AttractorshenonStrange attractor discovered by Michel Hénon
Line Shapeshilbert_jsDraws a Hilbert curve, a fractal space-filling curve.
AttractorshopalongHopalong attractor, also known as the Martin map
Line Shapeshtree_jsDraws an H-tree (made from lines in the shape of the letter H).
DiscidiscSwap polar coordinates ρ and θ, first taking the reciprocal of ρ.
Z ManipulationinflateZ_1Set z to tilt the plane forward, basing z mostly on y, but with some distortion
Z ManipulationinflateZ_2Set z to tilt the plane diagonally
Z ManipulationinflateZ_3Warp z to give a strong three dimensional effect
Z ManipulationinflateZ_4Set z to create interleaved helix shapes
Z ManipulationinflateZ_5Set z to give a gentle three dimensional wave shape
Z ManipulationinflateZ_6Set z to give a rolling shape
InversioninversionGeneralizes 2D circle inversion; same as spherical with the default parameters
PolarinvpolarTreat the rectangular coordinates (x,y) of a point as polar coordinates (ρ,θ) (the
inverse of polar)
Plottingisosfplot3d_wfIsosurface plot (plots points where the value of a function is near zero)
Polar Shapesjapanese_maple_leafShape resembling a Japanese maple leaf.
JuliajuliaClassic quadratic Julia set (deprecated; use julian with power=2)
Juliajulia3DClassic polynomial Julia set with 3D extrusion
Juliajulia3D_fl“Fluid” version of julia3D; allows fractional values for power
Juliajulia3DqJulia set using a rational power with 3D extrusion
Juliajulia3DzClassic polynomial Julia set with 3D extrusion
Juliajulia3Dz_fl“Fluid" version of julia3Dz; allows fractional values for power
JuliajuliacJulia set using a complex power
JuliajuliacomplexJulia set using a complex power
JuliajulianClassic polynomial Julia set
Juliajulian_fl“Fluid” version of julian; allows fractional values for power
Juliajulian2Julian with an integrated affine transform
Juliajulian2dcJulian2 with direct color
Juliajulian3DxJulian2 with 3D wave effect
JuliajuliaNabVariant of julian with different parameters
JuliajuliaqJulia set using a rational power
FlipperslazysensenDivide the flame into strips and flip them.
Line Shapeskoch_jsDraws a Koch curve.
Line ShapeslineA straight line.
LinearlinearCopy the input (x and y only)
Linearlinear3DCopy the input (x, y, and z)
LinearlinearTTweak of linear, adding an exponent for x and y
LinearlinearT3DTweak of linear3D, adding an exponent for x, y, and z
Line ShapeslissajousA Lissajous curve (named for Jules-Antoine Lissajous, who studied them).
L-Systemslsystem_jsCreate a two dimensional shape using an L-System. Compatible with the Fractint L-System
type
L-Systemslsystem3D_jsCreate a three dimensional mesh using an L-System.
Attractorslorenz_jsStrange attractor first studied by Edward Lorenz
AttractorsloziStrange attractor discovered by René Lozi
AttractorsmacmillanPerturbed McMillan map (studied by Edwin McMillan)
PatternsmandalaGenerate a fractal kaleidoscope pattern based on rotation transformations and rounding errors.
Polar Shapesmaple_leafShape resembling a maple leaf.
Maurer Linesmaurer_linesGeneralized string art
Rosecurvemaurer_roseString art on a rose curve
Shape Groupsmetaballs3d_wfA group of metaballs,balls (solid spheres) that merge when close to each other to form blobs.
FlippersminkowscopeFlip the plane in a wave shape based on the Minkowsky question-mark function across the origin.
ShapesnBlurPolygon shaped blur
ReshapersngonReshape circles centered at the origin into polygons, with an option for inversion
BlurrynoiseAdd noise as a blur effect
JulianpolarMashup of julian and polar2
Shape GroupsnsudokuA 9×9 grid of nested polygons, with coloring based on sudoku.
Polar Shapesoak_leafShape resembling an oak leaf.
Meshesobj_mesh_primitive_wfUse a predefined object as a 3D mesh
Importersobj_mesh_wfLoad a 3D mesh from an OBJ format file
FlippersoscilloscopeFlip the plane in a sine wave shape across the x axis.
Flippersoscilloscope2Flip the plane in a sine wave shape across the origin with perturbation.
InversionovoidSpherical with x and y scaling
Inversionovoid3DSpherical with x, y, and z scaling
Plottingparplot2d_wfParametric equation surface plot (2D surface plotted in three dimensions)
AttractorspdjPeter de Jong attractor
Juliaphoenix_juliaJulian with extra distortion parameters
ShapespieA circle with wedges missing, like pieces of pie
Shapespie_flFluid version of pie, allows fractional value for slices
Shapespie3DThree dimensional version of pie
Blurrypixel_flowBlur effect resembling flowing pixels
PolarpolarTreat the polar coordinates (ρ,θ) of a point as rectangular coordinates (x,y)
Polarpolar2Treat the log-polar coordinates (ρ,θ) of a point as rectangular coordinates (x,y)
Polarpolar2_3DVariant of polar2 with added 3D wave
Plottingpolarplot2d_wfPlot, in polar coordinates, rho in terms of theta, with 3D extrusion
Plottingpolarplot3d_wfPlot rho in terms of theta and phi (spherical coordinates) or theta and (cylindrical coordinates)
Symmetrypost_axis_symmetry_wfMirror the flame across the x, y, or z axis, with rotation.
Z Manipulationpost_bumpmap_wfSet z from an external bumpmap image
Symmetrypost_mirror_wfMirror the flame across the x, y, and/or z axes.
Symmetrypost_point_symmetry_wfMirror the flame across the x, y, and/or z axes.
Polarpost_polar2Treat the log-polar coordinates (ρ,θ) of a point as rectangular coordinates (x,y)
Inversionpost_sphericalReflects the plane across the unit circle
Inversionpost_zscaleMultiply the z value by the variation amount
Z Manipulationpost_ztranslateAdd the variation amount to z, translating points up or down the z axis
RosecurvepRose3DRose curve with three dimensional shaping
Shapespre_blurPre version of gaussian_blur
Boarderspre_boarders2Adds some parameters to boarders
Discpre_discSwap polar coordinates ρ and θ.
Discpre_disc3dSwap 2D polar coordinates ρ and θ and transforms z according to the distance from
the origin.
Polarpre_polar2Treat the log-polar coordinates (ρ,θ) of a point as rectangular coordinates (x,y)
Polarpre_polar2_yFlawed attempt at a pre version of polar2
Inversionpre_sphericalReflects the plane across the unit circle
Z Manipulationpre_zscaleMultiply the z value by the variation amount
Z Manipulationpre_ztranslateAdd the variation amount to z, translating points up or down the z axis
Reshapersprepost_circlizeCirclize before and uncirclize after other variations, or vice versa
Shapesprimitives_wfBlur with selectable two or three dimensional shape
RosecurvepRose3DRose curve with three dimensional shaping
Blurryradial_blurBlur effect rotating around the origin
FlippersrectanglesDivide the plane into rectangles and flip each horizontally and vertically.
RosecurverhodoneaAdvanced rose curve
RosecurveroseModulate a flame using the rose curve
Rosecurverose_wfSimple rose curve
Line Shapesrsquares_jsDraws a pattern of recursively placed squares.
Attractorssattractor3DGenerate a 3D mesh from differential equations
Attractorssattractor_jsA strange attractor attributed to Roger Bagula
FlippersscramblyDivide the central square into subsquares and scramble them.
SplittersseparationSplits the plane along the x and y axes, squishing or stretching the half planes.
Polar ShapesshapeGeneral shape generator using the superformula
ShreddersshreddedShreds the flame into strips in the x, y, and z directions and scrambles them.
ShreddersshredlinDivides the plane into horizontal and vertical strips and shrinks them.
ShreddersshredradDivides the plane into wedges and shrinks them
ShapessineblurA circle with a shading effect
Shapessphereblur3D version of sineblur
InversionsphericalReflects the plane across the unit circle
Inversionspherical3DA 3D version of spherical
Inversionspherical3D_wfA 3D version of spherical
Line ShapesspirographA Spirograph figure (epitrochoid or hypotrochoid).
Line Shapesspirograph3DA 3D Spirograph figure.
FlipperssplitSplit the plane into horizontal and vertical strips and flip alternate strips across the x and y
axes.
SplitterssplitsSplits the plane along the x and y axes, moving the half planes evenly.
Splitterssplits3DSplits the flame along the x, y, and z axes.
SplittersspligonDivide the plane into wedges and move them apart and around, leaving a polygon in the center.
Patternssnowflake_wfGenerate a snowflake shape using a cellular automaton.
ShapessquareSquare shaped blur
Shapessquare3DCube shaped blur
ReshaperssquarizeReshape circles centered at the orgin into squares
ShapesstarblurStar shaped blur
Importerssubflame_wfUse a flame as a shape.
PatternssunflowerGenerate a spiral of small polygons that can resemble the center of a sunflower.
Reshaperssuper_shapeReshape (or create a shape) using the superformula
ShapessuperShape3dGeneral 3D shape generator using two superformula instances
Attractorssvensson_jsJohnny Svensson attractor
Importerssvg_wfImport a Scalable Vector Graphics (SVG) file.
Symmetrysym_bg1To make the copies overlap, set stepx=-1 and stepy=0. Then adjust the parameters to achieve the desired positioning.
SynthsynthCombo variation (emulates several others) with added wave functions
Symmetrty outline: 0px;text-underline-position: under" rel="noopener">sym_bg1Make two identical copies of the flame.
Symmetrtysym_bg2Make two copies of the flame, the original and a horizontal reflection.
Symmetrtysym_bg3Make two copies of the flame, the original and a 180° rotation.
Symmetrtysym_bg4Make two copies of the flame, the original and a vertical reflection.
Symmetrtysym_bg5Make two copies of the flame, the original and a horizontal reflection.
Symmetrtysym_bg6Make four copies of the flame, the original, a vertical reflection, a horizontal reflection, and
a 180° rotation.
Symmetrtysym_bg7Make four copies of the flame, the original, a vertical reflection, a horizontal reflection, and
a 180° rotation.
Symmetrtysym_ng1Make two identical copies of the flame.
Symmetrtysym_ng2Make two copies of the flame, the original and a horizontal reflection.
Symmetrtysym_ng3Make two copies of the flame, the original and a 180° rotation.
Symmetrtysym_ng4Make four copies of the flame, the original, a vertical reflection, a horizontal reflection, and
a 180° rotation.
Symmetrtysym_ng5Make four copies of the flame, the original, a vertical reflection, a horizontal reflection, and
a 180° rotation.
Symmetrtysym_ng6Make four copies of the flame, two of the original and two horizontal reflections.
Symmetrtysym_ng7Make two copies of the flame, the original and a horizontal reflection.
Symmetrtysym_ng8Make eight copies of the flame, two each of the original, a vertical reflection, a horizontal
reflection, and a 180° rotation.
  
Symmetrtysym_ng9Make four copies of the flame, the original, a vertical reflection, a horizontal reflection, and
a 180° rotation.
Symmetrtysym_ng10Make four copies of the flame at 90° angles from each other.
Symmetrtysym_ng11Make eight copies of the flame, four at 90° angles from each other, and reflections of each of
these.
Symmetrtysym_ng12Make eight copies of the flame, four at 90° angles from each other, and reflections of each of these.
Symmetrtysym_ng13Make six copies of the flame, two each at 120° angles from each other, all with a horizonal
reflection.
Symmetrtysym_ng14Make twelve copies of the flame, two each at 120° angles from each other, plus horizontal
reflections of each.
Symmetrtysym_ng15Make twelve copies of the flame, two each at 120° angles from each other, plus horizontal
reflections of each.
Symmetrtysym_ng16Make twelve copies of the flame, two each at 60° angles from each other.
Symmetrtysym_ng17Make 24 copies of the flame, two each at 60° angles from each other, plus horizontal reflections of each.
PatternsszubietaFractal patterns by Santiago Zubieta: circle squares and square tile.
Patternsterrain3DGenerate a random terrain surface mesh
Shape GroupstapratsGenerate an Islamic style tiling (based on code from the “taprats” program).
Importerstext_wfA line of arbitrary text
AttractorsthreeplyA strange attractor named Three Ply
FlipperstradeTrade a circle on the right with a circle on the left, flipping them in the process.
Boarderstri_boarders2Divide the plane into hexagons with borders
ShapestriangleTriangular blur (3D)
Line Shapestree_jsDraws a fractal tree.
FlipperstqmirrorDivide the plane into four regions using right angles; shift one region and flip or rotate the
others.
PolarunpolarTreat the rectangular coordinates (x,y) of a point as log-polar coordinates (ρ,θ) (the
opposite of polar2)
WavesvibrationAdd sine waves in two arbitrary directions
Wavesvibration2Add sine waves in two arbitrary directions with modulation
PatternswangtilesGenerate a (possibly repeating) pattern from a 12×8 set of Wang tiles.
Shapeswaveblur_wfCreates waves, like ripples in a pond
WaveswavesAdd sine waves to x and y (dependent variation)
Waveswaves2Add sine waves to x and y
Waveswaves2_3DAdd sine waves to x and y with 3D addition
Waveswaves2_radialAdd sine waves to x and y outside a circle centered at the origin
Waveswaves2_wfAdd damped sine or cosine waves to x and y
Waveswaves22Add sine waves to x and y with power option
Waveswaves23Add triangular “waves” to x and y
Waveswaves2bAdd sine waves to x and y with scaling based on distance from center
Waveswaves3Add modulated sine waves to x and y
Waveswaves3_wfAdd damped squared sine or cosine waves to x and y
Waveswaves4Add sine waves to x and y with fracturing of horizontal wave
Waveswaves4_wfAdd damped cubed sine or cosine waves to x and y
Waveswaves42Add sine waves to x and y with fracturing of horizontal wave
WaveswavesD2Add damped sine or cosine waves to x and y
WaveswavesD3Add damped squared sine or cosine waves to x and y
WaveswavesD4Add damped cubed sine or cosine waves to x and y
WaveswavesnAdd damped waves to polynomial Julia set (aka julian)
DiscwdiscSwap polar coordinates ρ and θ, first taking the reciprocal of ρ, afterwards flipping the bottom half.
ReshapersxheartReshape circles centered at the origin into hearts
Shapesxheart_blur_wfHeart shaped blur
BoardersxtrbDivide the plane into hexagons with borders; tri_boarders2 with extra parameters
Plottingyplot2d_wfPlot y in terms of x, with 3D extrusion
Plottingyplot3d_wfPlot y in terms of x and z
ShapeszblurGaussian blur for the z axis only (no effect on x or y)
Z ManipulationzconeAdd the x-y distance of each point to z, thus transforming the plane into a cone
Z ManipulationztranslateAdd the variation amount to z, translating points up or down the z axis
Line ShapesZ_archA double arch.
Line ShapesZ_conicConic section shape (ellipse, parabola, or hyperbola)
From a list compiled by Rick Sidwell, variations with a brief description and what group they are in, i.e. what type of variation. Thank you Rick who originally created all this information. Clicking on the variation name will take you to the page for more information.

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