Variation List

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Flame Fractal Variations

Background Information

This information is copyright 2020 by Richard D. 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 here, 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.

VariationDescription
augerWave effect that gets stronger further from the origin
bi_linearSwap x and y
blobPushes and pulls the plane using a radial sine wave to make it look like a blob
blob_fl“Fluid” version of blob; allows fractional values for waves
blob2Modulate a flame using radial sine waves
blob3DA variant of blob that adds a 3D component
blurCircle with a bright center
blur_circleCircle with even coloring
blur_heartCreates a heart from two ellipses
blur_linearCreate a motion blur effect
blur_pixelizeAverages colors in an area to make large square pixels
blur_zoomCreate a zoom blur effect
blur3DThree dimensional Gaussian blur
boardersDivide the plane into squares with borders
boarders2Divide the plane into squares with borders, with parameters
butterflyReshape squares centered at the origin into butterfly shapes
cannabiscurve_wfShape resembling a cannabis leaf
chrysanthemumChrysanthemum flower shaped curve
cloverleaf_wfShape resembling a four leaf clover
circleblurCircle with even coloring
circlizeReshape squares centered at the origin into circles
circlize2Reshape squares centered at the origin into circles (scaled to work better with other variations)
clifford_jsStrange attractor attributed to Cliff Pickover
conic/conic2Conic section shape (ellipse, parabola, or hyperbola)
cpowRaise input point to a complex power specified by its real and imaginary parts
cpow2Raise input point to a complex power specified in polar coordinates
cpow3Raise input point to a complex power to produce a spiral
cpow3_wfAttempt to port cpow2 to JWildfire that “by happy accident became something else”
d_sphericalCombines spherical and linear
dc_boardersPresumably, a direct color version of boarders, but it appears to be the same as boarders
dc_linearDirect color version of linear3D
drosteImplements Escher’s map using logarithms; same effect as escher
eJuliaPolynomial Julia sets in elliptic coordinates
epispiralAn inside-out rose curve, known as an epispiral curve
epispiral_wfAlternate version of epispiral
escherImplements Escher’s Map
exblurBlur effect radiating from a point
extrudeExtrude the other variations on the transform by stretching the z coordinate
fanDivides the plane into pie shaped wedges and rotates them (dependent variation).
fan2Divides the plane into pie shaped wedges and rotates them.
flattenFlatten the flame by setting the z coordinate to 0
flipcircleFlips the points inside a circle centered at the origin top to bottom.
flipyFlips the points on the right side of the y-axis top to bottom.
flowerFilled-in rose curve; looks like a flower with petals
flower_dbReshape a flame into a 3D flower
flower2Filled-in rose curve; looks like a flower with petals
flower3DExperimental 3D version of flower
gaussian_blurFuzzy circle with a bright center, made from a Gaussian distribution
gingerbread_manAn attractor that resembles a gingerbread man
glitchy1Mix of lazysensen (divide flame into strips and flip them) and pixel_flow (blur to resemble flowing pixels).
gumowski_miraThe strange attractor of Gumowski-Mira
henonStrange attractor discovered by Michel Hénon
hopalongHopalong attractor, also known as the Martin map
inflateZ_1Set z to tilt the plane forward, basing z mostly on y, but with some distortion
inflateZ_2Set z to tilt the plane diagonally
inflateZ_3Warp z to give a strong three dimensional effect
inflateZ_4Set z to create interleaved helix shapes
inflateZ_5Set z to give a gentle three dimensional wave shape
inflateZ_6Set z to give a rolling shape
inversionGeneralizes 2D circle inversion; same as spherical with the default parameters
invpolarTreat the rectangular coordinates (x,y) of a point as polar coordinates (ρ,θ) (the inverse of polar)
isosfplot3d_wfIsosurface plot (plots points where the value of a function is near zero)
juliaClassic quadratic Julia set (deprecated; use julian with power=2)
julia3DClassic polynomial Julia set with 3D extrusion
julia3D_fl“Fluid” version of julia3D; allows fractional values for power
julia3DqJulia set using a rational power with 3D extrusion
julia3DzClassic polynomial Julia set with 3D extrusion
julia3Dz_fl“Fluid” version of julia3Dz; allows fractional values for power
juliacJulia set using a complex power
juliacomplexJulia set using a complex power
julianClassic polynomial Julia set
julian_fl“Fluid” version of julian; allows fractional values for power
julian2Julian with an integrated affine transform
julian2dcJulian2 with direct color
julian3DxJulian2 with 3D wave effect
juliaNabVariant of julian with different parameters
juliaqJulia set using a rational power
lazysensenDivide the flame into strips and flip them.
linearCopy the input (x and y only)
linear3DCopy the input (x, y, and z)
linearTTweak of linear, adding an exponent for x and y
linearT3DTweak of linear3D, adding an exponent for x, y, and z
lsystem_jsCreate a two dimensional shape using an L-System. Compatible with the Fractint L-System type
lsystem3D_jsCreate a three dimensional mesh using an L-System.
lorenz_jsStrange attractor first studied by Edward Lorenz
loziStrange attractor discovered by René Lozi
macmillanPerturbed McMillan map (studied by Edwin McMillan)
maurer_linesGeneralized string art
maurer_roseString art on a rose curve
minkowscopeFlip the plane in a wave shape based on the Minkowsky question-mark function across the origin.
nBlurPolygon shaped blur
ngonReshape circles centered at the origin into polygons, with an option for inversion
noiseAdd noise as a blur effect
npolarMashup of julian and polar2
obj_mesh_primitive_wfUse a predefined object as a 3D mesh
obj_mesh_wfLoad a 3D mesh from an OBJ format file
oscilloscopeFlip the plane in a sine wave shape across the x axis.
oscilloscope2Flip the plane in a sine wave shape across the origin with perturbation.
ovoidSpherical with x and y scaling
ovoid3DSpherical with x, y, and z scaling
parplot2d_wfParametric equation surface plot (2D surface plotted in three dimensions)
pdjPeter de Jong attractor
phoenix_juliaJulian with extra distortion parameters
pieA circle with wedges missing, like pieces of pie
pie_flFluid version of pie, allows fractional value for slices
pie3DThree dimensional version of pie
pixel_flowBlur effect resembling flowing pixels
polarTreat the polar coordinates (ρ,θ) of a point as rectangular coordinates (x,y)
polar2Treat the log-polar coordinates (ρ,θ) of a point as rectangular coordinates (x,y)
polar2_3DVariant of polar2 with added 3D wave
polarplot2d_wfPlot, in polar coordinates, rho in terms of theta, with 3D extrusion
polarplot3d_wfPlot rho in terms of theta and phi (spherical coordinates) or theta and (cylindrical coordinates)
post_bumpmap_wfSet z from an external bumpmap image
post_julia3DqJulia set using a rational power with 3D extrusion
post_julian2Julian with an integrated affine transform
post_juliaqJulia set using a rational power
post_polar2Treat the log-polar coordinates (ρ,θ) of a point as rectangular coordinates (x,y)
post_sphericalReflects the plane across the unit circle
post_zscaleMultiply the z value by the variation amount
post_ztranslateAdd the variation amount to z, translating points up or down the z axis
pre_blurPre version of gaussian_blur
pre_blur3DThree dimensional Gaussian blur
pre_boarders2Adds some parameters to boarders
pre_polar2Treat the log-polar coordinates (ρ,θ) of a point as rectangular coordinates (x,y)
pre_polar2_yFlawed attempt at a pre version of polar2
pre_sphericalReflects the plane across the unit circle
pre_zscaleMultiply the z value by the variation amount
pre_ztranslateAdd the variation amount to z, translating points up or down the z axis
prepost_circlizeCirclize before and uncirclize after other variations, or vice versa
primitives_wfBlur with selectable two or three dimensional shape
pRose3DRose curve with three dimensional shaping
radial_blurBlur effect rotating around the origin
rectanglesDivide the plane into rectangles and flip each horizontally and vertically.
rhodoneaAdvanced rose curve
roseModulate a flame using the rose curve
rose_wfSimple rose curve
sattractor3DGenerate a 3D mesh from differential equations
sattractor_jsA strange attractor attributed to Roger Bagula
scramblyDivide the central square into subsquares and scramble them.
shapeGeneral shape generator using the superformula
sineblurA circle with a shading effect
sphereblur3D version of sineblur
sphericalReflects the plane across the unit circle
spherical3DA 3D version of spherical
spherical3D_wfA 3D version of spherical
splitSplit the plane into horizontal and vertical strips and flip alternate strips across the x and y axes.
squareSquare shaped blur
square3DCube shaped blur
squarizeReshape circles centered at the orgin into squares
starblurStar shaped blur
super_shapeReshape (or create a shape) using the superformula
superShape3dGeneral 3D shape generator using two superformula instances
svensson_jsJohnny Svensson attractor
synthCombo variation (emulates several others) with added wave functions
terrain3DGenerate a random terrain surface mesh
threeplyA strange attractor named Three Ply
tradeTrade a circle on the right with a circle on the left, flipping them in the process.
tri_boarders2Divide the plane into hexagons with borders
triangleTriangular blur (3D)
tqmirrorDivide the plane into four regions using right angles; shift one region and flip or rotate the others.
unpolarTreat the rectangular coordinates (x,y) of a point as log-polar coordinates (ρ,θ) (the opposite of polar2)
vibrationAdd sine waves in two arbitrary directions
vibration2Add sine waves in two arbitrary directions with modulation
waveblur_wfCreates waves, like ripples in a pond
wavesAdd sine waves to x and y (dependent variation)
waves2Add sine waves to x and y
waves2_3DAdd sine waves to x and y with 3D addition
waves2_radialAdd sine waves to x and y outside a circle centered at the origin
waves2_wfAdd damped sine or cosine waves to x and y
waves22Add sine waves to x and y with power option
waves23Add triangular “waves” to x and y
waves2bAdd sine waves to x and y with scaling based on distance from center
waves3Add modulated sine waves to x and y
waves3_wfAdd damped squared sine or cosine waves to x and y
waves4Add sine waves to x and y with fracturing of horizontal wave
waves4_wfAdd damped cubed sine or cosine waves to x and y
waves42Add sine waves to x and y with fracturing of horizontal wave
wavesD2Add damped sine or cosine waves to x and y
wavesD3Add damped squared sine or cosine waves to x and y
wavesD4Add damped cubed sine or cosine waves to x and y
wavesnAdd damped waves to polynomial Julia set (aka julian)
xheartReshape circles centered at the origin into hearts
xheart_blur_wfHeart shaped blur
xtrbDivide the plane into hexagons with borders; tri_boarders2 with extra parameters
yplot2d_wfPlot y in terms of x, with 3D extrusion
yplot3d_wfPlot y in terms of x and z
zblurGaussian blur for the z axis only (no effect on x or y)
zclearFlatten the flame by setting the z coordinate to 0
zconeAdd the x-y distance of each point to z, thus transforming the plane into a cone
zscaleMultiply the z value by the variation amount
ztranslateAdd the variation amount to z, translating points up or down the z axis
Z_conicConic section shape (ellipse, parabola, or hyperbola)
Z_flowerFilled-in rose curve; looks like a flower with petals

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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