# Flame Fractal Variations – Rick Sidwell

## Variations and their Types

### Notes by 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, or by group (type of variation).

Variation | Types | Description |
---|---|---|

arch | Line Shapes | A double arch. |

auger | Waves | Wave effect that gets stronger further from the origin |

bi_linear | Linear | Swap x and y |

blob | Blobs | Pushes and pulls the plane using a radial sine wave to make it look like a blob. |

blob_fl | Blobs | “Fluid” version of blob; allows fractional values for waves |

blob2 | Blobs | Modulate a flame using radial sine waves. |

blob3D | Blobs | A variant of blob that adds a 3D component. |

blur | Shapes | Circle with a bright centre. |

blur_circle | Shapes | Circle with even coloring. |

blur_heart | Shapes | Creates a heart from two ellipses. |

blur_linear | Blurry | Create a motion blur effect. |

blur_pixelize | Blurry | Averages colors in an area to make large square pixels. |

blur_zoom | Blurry | Create a zoom blur effect. |

blur3D | Shapes | Three dimensional Gaussian blur. |

boarders | Boarders | Divide the plane into squares with borders. |

boarders2 | Boarders | Divide the plane into squares with borders, with parameters. |

butterfly | Reshapers | Reshape squares centered at the origin into butterfly shapes. |

butterfly_fay | Line Shapes | A butterfly shaped curve discovered by Temple H Fay in 1989. |

cannabiscurve_wf | Polar Shapes | Shape resembling a cannabis leaf. |

checkerboard_wf | Patterns | Generate a checkerboard pattern. |

checks | Shredders | Divides the flame into a checkerboard and shifts half of the squares up and left and the other half down and right. |

chrysanthemum | Shapes | Chrysanthemum flower shaped curve. |

cloverleaf_wf | Polar Shapes | Shape resembling a four leaf clover. |

circleblur | Shapes | Circle with even coloring. |

circlize | Reshapers | Reshape squares centered at the origin into circles. |

circlize2 | Reshapers | Reshape squares centered at the origin into circles (scaled to work better with other variations) |

circleRand | Shape Groups | Random size circles in a grid. |

circlesplit | Splitters | Split the flame in a circle centered at the origin. |

circus | Splitters | Scale the unit circle and the the rest of the flame separately. |

clifford_js | Attractors | Strange attractor attributed to Cliff Pickover |

colormap_wf / post_colormap_wf | Importers | Load colors from an external image. |

conic/conic2 | Polar Shapes | Conic section shape (ellipse, parabola, or hyperbola) |

corners | Splitters | Splits the plane along the x and y axes and stretches it as if tugging the corners. |

cpow | Cpow | Raise input point to a complex power specified by its real and imaginary parts |

cpow2 | Cpow | Raise input point to a complex power specified in polar coordinates |

cpow3 | Cpow | Raise input point to a complex power to produce a spiral |

cpow3_wf | Cpow | Attempt to port cpow2 to JWildfire that Â "by happy accident became something else" |

dc_linear | Linear | Direct color version of linear3D. |

d_spherical | Inversion | Combines spherical and linear |

disc | Disc | Swap polar coordinates ρ and θ. |

disc2 | Disc | Swap polar coordinates ρ and θ, but using Manhattan distance instead of Euclidean. |

disc3 | Disc | Swap polar coordinates ρ and θ, with parameters. |

disc3d | Disc | Swap 2D polar coordinates ρ and θ and transforms z according to the distance from the origin. |

dc_acrilic | Stamps | Create a pattern reminiscent of acrylic pour painting. |

dc_apollonian | Stamps | Create a colorful pattern. |

dc_boarders | Boarders | Presumably, a direct color version of boarders, but it appears to be the same as boarders. |

dc_booleans | Stamps | Creates patterns based on boolean operators. |

dc_butterflies | Stamps | Creates butterfly patterns using a Nova fractal |

dc_cairotiles | Stamps | Create patterns from rotated squares in a grid. |

dc_circlesblue | Stamps | Create random bubbles. |

dc_circuits | Stamps | Create a pattern reminiscent of a circuit board. |

dc_code | Stamps | Create a fractal picture, using arbitrary code. |

dc_ducks | Stamps | Create a fractal "ducks" pattern. |

dc_fingerprint | Stamps | Create a pattern resembling a fingerprint. |

dc_fractaldots | Stamps | Create a pattern from fractally arranged dots. |

dc_gabornoise | Stamps | Generate a pattern resembling Gabor noise. |

dc_glypho | Stamps | Generate a pattern based on rings of nested circles. |

dc_grid3D | Stamps | Generate a 2D image of a 3D grid. |

dc_hexagons | Stamps | Generate a hexagon grid pattern. |

dc_hoshi | Stamps | Create a design based on fractal hoshi tiling. |

dc_hyperbolictile | Stamps | Create a {3,8} hyperbolic tessellation mapped to a Poincare disk. |

dc_inversion | Stamps | Create a fractal design based on circle inversion. |

dc_kaleidocomplex | Stamps | Generate a kaleidoscopic pattern. |

dc_kaleidoscopic | Stamps | Generate a kaleidoscopic pattern. |

dc_kaliset | Stamps | Generate a pattern using Kalisets. |

dc_kaliset2 | Stamps | Generate a pattern using kalisets. |

dc_layers | Stamps | Create a layered pattern of wavy circles. |

dc_mandala | Stamps | Create a kaleidoscopic mandala pattern. |

dc_mandbrot | Stamps | Create a kaleidoscopic pattern based on the Mandelbrot set. |

dc_mandelbox2D | Stamps | Create a two dimensional Mandelbox pattern. |

dc_menger | Stamps | Generate a Sierpiński carpet pattern (looks like the face of a Menger sponge). |

dc_moebiuslog | Stamps | Create a spiraling pattern using log and a MÃ¶bius transform. |

dc_pentatiles | Stamps | Generate a pattern of tiled pentagons. |

dc_poincaredisc | Stamps | Generate a hyperbolic tiling mapped to a Poincare disk. |

dc_quadtree | Stamps | Create a graphical display of a random quadtree. |

dc_randomoctree | Stamps | Create a graphical (2D) display of a random (3D) octree. |

dc_rotations | Stamps | Create a pattern using repeated rotations. |

dc_spacefold | Stamps | Create a pattern using a space folding technique. |

dc_squares | Stamps | Create a pattern of squares on a grid. |

dc_starsfield | Stamps | Create a field of stars. |

dc_sunflower | Stamps | Create a pattern of spirals. |

dc_tesla | Stamps | Create a pattern resembling electrical arcing. |

dc_tree | Stamps | Generate a tree shape. |

dc_triantess | Stamps | Construct a tiling using Wythoff construction. |

dc_truchet | Stamps | Generate a truchet tiling pattern. |

dc_turbulence | Stamps | Generate a turbulence noise pattern. |

dc_voronoise | Stamps | Generate a pattern based on a combination of Voronoi diagrams and noise. |

dc_vortex | Stamps | Create a pattern from a train of vortices. |

dc_warping | Stamps | Generate a texture using fBm warping. |

dc_worley | Stamps | |

dc_linear | Linear | Direct color version of linear3D |

dc_perlin | Patterns | Generate a pattern based on fractal Brownian motion (fBm), also known as Perlin noise. |

dla_wf | Patterns | Create a simple Diffusion Limited Aggregation (DLA) pattern. |

dla3d_wf | Patterns | Create a 3D Diffusion Limited Aggregation (DLA) mesh. |

dragon_js | Line Shapes | Draws a Heighway dragon curve. |

droste | Cpow | Implements Eschers map using logarithms; same effect as escher |

edisc | Disc | Swap elliptic coordinates μ and ν. |

eJulia | Julia | Polynomial Julia sets in elliptic coordinates |

epispiral | Rosecurve | An inside-out rose curve, known as an epispiral curve |

epispiral_wf | Rosecurve | Alternate version of epispiral |

escher | Cpow | Implements Escher’s Map |

exblur | Blurry | Blur effect radiating from a point |

extrude | Z manipulation | Extrude the other variations on the transform by stretching the z coordinate |

fan | Flippers | Divides the plane into pie shaped wedges and rotates them (dependent variation). |

fan2 | Flippers | Divides the plane into pie shaped wedges and rotates them. |

fdisc | Disc | Swap polar coordinates ρ and θ, first taking the reciprocal of ρ; scales by 2𝜋 instead of 𝜋. |

flatten | Z manipulation | Flatten the flame by setting the z coordinate to 0 |

flipcircle | Flippers | Flips the points inside a circle centred at the origin top to bottom. |

flipy | Flippers | Flips the points on the right side of the y-axis top to bottom. |

flower | Rosecurve | Filled-in rose curve; looks like a flower with petals |

flower_db | Blobs | Reshape a flame into a 3D flower |

flower3D | Rosecurve | Experimental 3D version of flower |

gaussian_blur | Shapes | Fuzzy circle with a bright center, made from a Gaussian distribution |

gingerbread_man | Attractors | An attractor that resembles a gingerbread man |

glitchy1 | Flippers | Mix of (divide flame into strips and flip them) and (blur to resemble flowing pixels). |

glsl_acrilic | Stamps | Create a pattern reminiscent of acrylic pour painting. |

glsl_apollonian | Stamps | Create a colorful pattern. |

glsl_circlesblue | Stamps | Create random bubbles. |

glsl_circuits | Stamps | Create a pattern reminiscent of a circuit board. |

glsl_code | Stamps | Create a fractal picture, using arbitrary code. |

glsl_fractaldots | Stamps | Create a pattern from fractally arranged dots. |

glsl_grid3D | Stamps | Generate a 2D image of a 3D grid. |

glsl_hoshi | Stamps | Create a design based on fractal hoshi tiling. |

glsl_hyperbolictile | Stamps | Create a {3,8} hyperbolic tessellation mapped to a PoincarÃ© disk. |

glsl_kaleidocomplex | Stamps | Generate a kaleidoscopic pattern. |

glsl_kaleidoscopic | Stamps | Generate a kaleidoscopic pattern. |

glsl_kaliset | Stamps | Generate a pattern using Kalisets. |

glsl_kaliset2 | Stamps | Generate a pattern using Kalisets. |

glsl_mandala | Stamps | Create a kaleidoscopic mandala pattern. |

glsl_mandelbox2D | Stamps | Create a two dimensional Mandelbox pattern. |

glsl_randomoctree | Stamps | Create a graphical (2D) display of a random (3D) octree |

glsl_squares | Stamps | Create a pattern of squares on a grid. |

glsl_starsfield | Stamps | Create a field of stars. |

gosper_js | Line Shapes | Draws a Gosper island curve, also known as a flowsnake. |

gpattern | Shape Groups | A grid pattern of polygons. |

gumowski_mira | Attractors | The strange attractor of Gumowski-Mira |

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

harmonograph_js | Line Shapes | Figures that might be made from a swinging pendulum on a harmonograph. |

henon | Attractors | Strange attractor discovered by Michel HÃ©non |

hilbert_js | Line Shapes | Draws a Hilbert curve, a fractal space-filling curve. |

hopalong | Attractors | Hopalong attractor, also known as the Martin map |

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

idisc | Disc | Swap polar coordinates ρ and θ, first taking the reciprocal of ρ. |

inflateZ_1 | Z manipulation | Set z to tilt the plane forward, basing z mostly on y, but with some distortion |

inflateZ_2 | Z manipulation | Set z to tilt the plane diagonally |

inflateZ_3 | Z manipulation | Warp z to give a strong three dimensional effect |

inflateZ_4 | Z manipulation | Set z to create interleaved helix shapes |

inflateZ_5 | Z manipulation | Set z to give a gentle three dimensional wave shape |

inflateZ_6 | Z manipulation | Set z to give a rolling shape |

inversion | Inversion | Generalizes 2D circle inversion; same as spherical with the default parameters |

invpolar | Polar | Treat the rectangular coordinates (x,y) of a point as polar coordinates (ρ,θ) (the inverse of polar) |

isosfplot3d_wf | Plotting | Isosurface plot (plots points where the value of a function is near zero) |

japanese_maple_leaf | Polar Shapes | Shape resembling a Japanese maple leaf. |

julia | Julia | Classic quadratic Julia set (deprecated; use julian with power=2) |

julia3D | Julia | Classic polynomial Julia set with 3D extrusion |

julia3D_fl | Julia | “Fluid” version of julia3D; allows fractional values for power |

julia3Dq | Julia | Julia set using a rational power with 3D extrusion |

julia3Dz | Julia | Classic polynomial Julia set with 3D extrusion |

julia3Dz_fl | Julia | “Fluid" version of julia3Dz; allows fractional values for power |

juliac | Julia | Julia set using a complex power |

juliacomplex | Julia | Julia set using a complex power |

julian | Julia | Classic polynomial Julia set |

julian_fl | Julia | “Fluid” version of julian; allows fractional values for power |

julian2 | Julia | Julian with an integrated affine transform |

julian2dc | Julia | Julian2 with direct color |

julian3Dx | Julia | Julian2 with 3D wave effect |

juliaNab | Julia | Variant of julian with different parameters |

juliaq | Julia | Julia set using a rational power |

lazysensen | Flippers | Divide the flame into strips and flip them. |

koch_js | Line Shapes | Draws a Koch curve. |

line | Line Shapes | A straight line. |

linear | Linear | Copy the input (x and y only) |

linear3D | Linear | Copy the input (x, y, and z) |

linearT | Linear | Tweak of linear, adding an exponent for x and y |

linearT3D | Linear | Tweak of linear3D, adding an exponent for x, y, and z |

lissajous | Line Shapes | A Lissajous curve (named for Jules-Antoine Lissajous, who studied them). |

lsystem_js | L-Systems | Create a two dimensional shape using an L-System. Compatible with the Fractint L-System type |

lsystem3D_js | L-Systems | Create a three dimensional mesh using an L-System. |

lorenz_js | Attractors | Strange attractor first studied by Edward Lorenz |

lozi | Attractors | Strange attractor discovered by RenÃ© Lozi |

macmillan | Attractors | Perturbed McMillan map (studied by Edwin McMillan) |

mandala | Patterns | Generate a fractal kaleidoscope pattern based on rotation transformations and rounding errors. |

maple_leaf | Polar Shapes | Shape resembling a maple leaf. |

maurer_lines | Maurer Lines | Generalized string art |

maurer_rose | Rosecurve | String art on a rose curve |

metaballs3d_wf | Shape Groups | A group of metaballs,balls (solid spheres) that merge when close to each other to form blobs. |

minkowscope | Flippers | Flip the plane in a wave shape based on the Minkowsky question-mark function across the origin. |

nBlur | Shapes | Polygon shaped blur |

ngon | Reshapers | Reshape circles centered at the origin into polygons, with an option for inversion |

noise | Blurry | Add noise as a blur effect |

npolar | Julia | Mashup of julian and polar2 |

nsudoku | Shape Groups | A 9Ã—9 grid of nested polygons, with coloring based on sudoku. |

oak_leaf | Polar Shapes | Shape resembling an oak leaf. |

obj_mesh_primitive_wf | Meshes | Use a predefined object as a 3D mesh |

obj_mesh_wf | Importers | Load a 3D mesh from an OBJ format file |

oscilloscope | Flippers | Flip the plane in a sine wave shape across the x axis. |

oscilloscope2 | Flippers | Flip the plane in a sine wave shape across the origin with perturbation. |

ovoid | Inversion | Spherical with x and y scaling |

ovoid3D | Inversion | Spherical with x, y, and z scaling |

parplot2d_wf | Plotting | Parametric equation surface plot (2D surface plotted in three dimensions) |

pdj | Attractors | Peter de Jong attractor |

phoenix_julia | Julia | Julian with extra distortion parameters |

pie | Shapes | A circle with wedges missing, like pieces of pie |

pie_fl | Shapes | Fluid version of pie, allows fractional value for slices |

pie3D | Shapes | Three dimensional version of pie |

pixel_flow | Blurry | Blur effect resembling flowing pixels |

polar | Polar | Treat the polar coordinates (ρ,θ) of a point as rectangular coordinates (x,y) |

polar2 | Polar | Treat the log-polar coordinates (ρ,θ) of a point as rectangular coordinates (x,y) |

polar2_3D | Polar | Variant of polar2 with added 3D wave |

polarplot2d_wf | Plotting | Plot, in polar coordinates, rho in terms of theta, with 3D extrusion |

polarplot3d_wf | Plotting | Plot rho in terms of theta and phi (spherical coordinates) or theta and (cylindrical coordinates) |

post_axis_symmetry_wf | Symmetry | Mirror the flame across the x, y, or z axis, with rotation. |

post_bumpmap_wf | Z manipulation | Set z from an external bumpmap image |

post_mirror_wf | Symmetry | Mirror the flame across the x, y, and/or z axes. |

post_point_symmetry_wf | Symmetry | Mirror the flame across the x, y, and/or z axes. |

post_polar2 | Polar | Treat the log-polar coordinates (ρ,θ) of a point as rectangular coordinates (x,y) |

post_spherical | Inversion | Reflects the plane across the unit circle |

post_zscale | Inversion | Multiply the z value by the variation amount |

post_ztranslate | Z manipulation | Add the variation amount to z, translating points up or down the z axis |

pRose3D | Rosecurve | Rose curve with three dimensional shaping |

pre_blur | Shapes | Pre version of gaussian_blur |

pre_boarders2 | Boarders | Adds some parameters to boarders |

pre_disc | Disc | Swap polar coordinates ρ and θ. |

pre_disc3d | Disc | Swap 2D polar coordinates ρ and θ and transforms z according to the distance from the origin. |

pre_polar2 | Polar | Treat the log-polar coordinates (ρ,θ) of a point as rectangular coordinates (x,y) |

pre_polar2_y | Polar | Flawed attempt at a pre version of polar2 |

pre_spherical | Inversion | Reflects the plane across the unit circle |

pre_zscale | Z manipulation | Multiply the z value by the variation amount |

pre_ztranslate | Z manipulation | Add the variation amount to z, translating points up or down the z axis |

prepost_circlize | Reshapers | Circlize before and uncirclize after other variations, or vice versa |

primitives_wf | Shapes | Blur with selectable two or three dimensional shape |

pRose3D | Rosecurve | Rose curve with three dimensional shaping |

radial_blur | Blurry | Blur effect rotating around the origin |

rectangles | Flippers | Divide the plane into rectangles and flip each horizontally and vertically. |

rhodonea | Rosecurve | Advanced rose curve |

rose | Rosecurve | Modulate a flame using the rose curve |

rose_wf | Rosecurve | Simple rose curve |

rsquares_js | Line Shapes | Draws a pattern of recursively placed squares. |

sattractor3D | Attractors | Generate a 3D mesh from differential equations |

sattractor_js | Attractors | A strange attractor attributed to Roger Bagula |

scrambly | Flippers | Divide the central square into subsquares and scramble them. |

separation | Splitters | Splits the plane along the x and y axes, squishing or stretching the half planes. |

shape | Polar Shapes | General shape generator using the superformula |

shredded | Shredders | Shreds the flame into strips in the x, y, and z directions and scrambles them. |

shredlin | Shredders | Divides the plane into horizontal and vertical strips and shrinks them. |

shredrad | Shredders | Divides the plane into wedges and shrinks them |

sineblur | Shapes | A circle with a shading effect |

sphereblur | Shapes | 3D version of sineblur |

spherical | Inversion | Reflects the plane across the unit circle |

spherical3D | Inversion | A 3D version of spherical |

spherical3D_wf | Inversion | A 3D version of spherical |

spirograph | Line Shapes | A Spirograph figure (epitrochoid or hypotrochoid). |

spirograph3D | Line Shapes | A 3D Spirograph figure. |

split | Flippers | Split the plane into horizontal and vertical strips and flip alternate strips across the x and y axes. |

splits | Splitters | Splits the plane along the x and y axes, moving the half planes evenly. |

splits3D | Splitters | Splits the flame along the x, y, and z axes. |

spligon | Splitters | Divide the plane into wedges and move them apart and around, leaving a polygon in the center. |

snowflake_wf | Patterns | Generate a snowflake shape using a cellular automaton. |

square | Shapes | Square shaped blur |

square3D | Shapes | Cube shaped blur |

squarize | Reshapers | Reshape circles centered at the orgin into squares |

starblur | Shapes | Star shaped blur |

subflame_wf | Importers | Use a flame as a shape. |

sunflower | Patterns | Generate a spiral of small polygons that can resemble the center of a sunflower. |

super_shape | Reshapers | Reshape (or create a shape) using the superformula |

superShape3d | Shapes | General 3D shape generator using two superformula instances |

svensson_js | Attractors | Johnny Svensson attractor |

svg_wf | Importers | Import a Scalable Vector Graphics (SVG) file. |

sym_bg1 | Symmetry | To make the copies overlap, set stepx=-1 and stepy=0. Then adjust the parameters to achieve the desired positioning. |

synth | SynSynthth | Combo variation (emulates several others) with added wave functions |

sym_bg1 | Symmetry | Make two identical copies of the flame. |

sym_bg2 | Symmetry | Make two copies of the flame, the original and a horizontal reflection. |

sym_bg3 | Symmetry | Make two copies of the flame, the original and a 180Â° rotation. |

sym_bg4 | Symmetry | Make two copies of the flame, the original and a vertical reflection. |

sym_bg5 | Symmetry | Make two copies of the flame, the original and a horizontal reflection. |

sym_bg6 | Symmetry | Make four copies of the flame, the original, a vertical reflection, a horizontal reflection, and a 180Â° rotation. |

sym_bg7 | Symmetry | Make four copies of the flame, the original, a vertical reflection, a horizontal reflection, and a 180Â° rotation. |

sym_ng1 | Symmetry | Make two identical copies of the flame. |

sym_ng2 | Symmetry | Make two copies of the flame, the original and a horizontal reflection. |

sym_ng3 | Symmetry | Make two copies of the flame, the original and a 180Â° rotation. |

sym_ng4 | Symmetry | Make four copies of the flame, the original, a vertical reflection, a horizontal reflection, and a 180Â° rotation. |

sym_ng5 | Symmetry | Make four copies of the flame, the original, a vertical reflection, a horizontal reflection, and a 180Â° rotation. |

sym_ng6 | Symmetry | Make four copies of the flame, two of the original and two horizontal reflections. |

sym_ng7 | Symmetry | Make two copies of the flame, the original and a horizontal reflection. |

sym_ng8 | Symmetry | Make eight copies of the flame, two each of the original, a vertical reflection, a horizontal reflection, and a 180Â° rotation. |

sym_ng9 | Symmetry | Make four copies of the flame, the original, a vertical reflection, a horizontal reflection, and a 180Â° rotation. |

sym_ng10 | Symmetry | Make four copies of the flame at 90Â° angles from each other. |

sym_ng11 | Symmetry | Make eight copies of the flame, four at 90Â° angles from each other, and reflections of each of these. |

sym_ng12 | Symmetry | Make eight copies of the flame, four at 90Â° angles from each other, and reflections of each of these. |

sym_ng13 | Symmetry | Make six copies of the flame, two each at 120Â° angles from each other, all with a horizonal reflection. |

sym_ng14 | Symmetry | Make twelve copies of the flame, two each at 120Â° angles from each other, plus horizontal reflections of each. |

sym_ng15 | Symmetry | Make twelve copies of the flame, two each at 120Â° angles from each other, plus horizontal reflections of each. |

sym_ng16 | Symmetry | Make twelve copies of the flame, two each at 60Â° angles from each other. |

sym_ng17 | Symmetry | Make 24 copies of the flame, two each at 60Â° angles from each other, plus horizontal reflections of each. |

szubieta | Patterns | Fractal patterns by Santiago Zubieta: circle squares and square tile. |

terrain3D | Patterns | Generate a random terrain surface mesh |

taprats | Shape Groups | Generate an Islamic style tiling (based on code from the Â“tapratsÂ” program). |

text_wf | Importers | A line of arbitrary text |

threeply | Attractors | A strange attractor named Three Ply |

trade | Flippers | Trade a circle on the right with a circle on the left, flipping them in the process. |

tri_boarders2 | Boarders | Divide the plane into hexagons with borders |

triangle | Shapes | Triangular blur (3D) |

tree_js | Line Shapes | Draws a fractal tree. |

tqmirror | Flippers | Divide the plane into four regions using right angles; shift one region and flip or rotate the others. |

unpolar | Polar | Treat the rectangular coordinates (x,y) of a point as log-polar coordinates (ρ,θ) (the opposite of polar2) |

vibration | Waves | Add sine waves in two arbitrary directions |

vibration2 | Waves | Add sine waves in two arbitrary directions with modulation |

wangtiles | Patterns | Generate a (possibly repeating) pattern from a 12Ã—8 set of Wang tiles. |

waveblur_wf | Shapes | Creates waves, like ripples in a pond |

waves | Waves | Add sine waves to x and y (dependent variation) |

waves2 | Waves | Add sine waves to x and y |

waves2_3D | Waves | Add sine waves to x and y with 3D addition |

waves2_radial | Waves | Add sine waves to x and y outside a circle centered at the origin |

waves2_wf | Waves | Add damped sine or cosine waves to x and y |

waves22 | Waves | Add sine waves to x and y with power option |

waves23 | Waves | Add triangular “waves” to x and y |

waves2b | Waves | Add sine waves to x and y with scaling based on distance from center |

waves3 | Waves | Add modulated sine waves to x and y |

waves3_wf | Waves | Add damped squared sine or cosine waves to x and y |

waves4 | Waves | Add sine waves to x and y with fracturing of horizontal wave |

waves4_wf | Waves | Add damped cubed sine or cosine waves to x and y |

waves42 | Waves | Add sine waves to x and y with fracturing of horizontal wave |

wavesD2 | Waves | Add damped sine or cosine waves to x and y |

wavesD3 | Waves | Add damped squared sine or cosine waves to x and y |

wavesD4 | Waves | Add damped cubed sine or cosine waves to x and y |

wavesn | Waves | Add damped waves to polynomial Julia set (aka julian) |

wdisc | Disc | Swap polar coordinates ρ and θ, first taking the reciprocal of ρ, afterwards flipping the bottom half. |

xheart | Reshapers | Reshape circles centered at the origin into hearts |

xheart_blur_wf | Shapes | Heart shaped blur |

xtrb | Boarders | Divide the plane into hexagons with borders; tri_boarders2 with extra parameters |

yplot2d_wf | Plotting | Plot y in terms of x, with 3D extrusion |

yplot3d_wf | Plotting | Plot y in terms of x and z |

zblur | Shapes | Gaussian blur for the z axis only (no effect on x or y) |

zcone | Z manipulation | Add the x-y distance of each point to z, thus transforming the plane into a cone |

ztranslate | Z manipulation | Add the variation amount to z, translating points up or down the z axis |

Z_arch | Line Shapes | A double arch. |

Z_conic | Line Shapes | Conic section shape (ellipse, parabola, or hyperbola) |

### Notes by Rick Sidwell

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.

Please don’t create issues for missing variations; I’m already aware most variations are missing.