HomeVariation TypesSymmetry

Symmetry

Variations that create multiple copies with various symmetrical variations. The examples for these variations show the letters “SYM” with the variation applied once to show the essence of each. All have parameters that will change the results.

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post_axis_symmetry_wf

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

Type: 3D
Author: Andreas Maschke (thargor6)
Date: 12 Oct 2015

ParameterDescription
axis0: Mirror across x axis
1: Mirror across y axis
2: Mirror across z axis
centre_x, centre_y, centre_zCenter point for mirror
rotationAngle to rotate flame before mirroring, in degrees
x1colorshift, y1colorshift, z1colorshiftAmount to shift the gradient index for the unmirrored flame for x, y, or z mirrors
x2colorshift, y2colorshift, z2colorshiftAmount to shift the gradient index for the mirrored flame for x, y, or z mirrors

post_mirror_wf

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

Type: 3D
Author: Andreas Maschke (thargor6)
Date: 8 Dec 2011

ParameterDescription
xaxis1 to mirror flame across x axis or 0 to skip
yaxis1 to mirror flame across y axis or 0 to skip
zaxis1 to mirror flame across z axis or 0 to skip
xshiftAmount to shift x mirror left (negative to shift right)
yshiftAmount to shift y mirror up (negative to shift down)
zshiftAmount to shift z mirror away (towards negative z)
xscale, yscaleHorizontal and vertical scale factors for mirrored instances; 1 for same size as original
xcolorshiftAmount to shift gradient index for x mirrors (0 to 1, 0 for none)
ycolorshiftAmount to shift gradient index for y mirrors (0 to 1, 0 for none)
zcolorshiftAmount to shift gradient index for z mirrors (0 to 1, 0 for none)

post_point_symmetry_wf

Rotational symmetry of any order around an arbitrary point.

Type: 2D
Author: Andreas Maschke (thargor6)
Date: 12 Oct 2015

ParameterDescription
centre_x, centre_yCenter point for the rotation
orderNumber of rotational copies; must be a positive integer
colorshiftAmount to shift gradient index for each copy

sym_bg1

Make two identical copies of the flame.

Type: 2D
Author: Jesus Sosa
Date: 5 May 2021

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

Sym_bg1 and sym_ng1 do the same thing, except the parameters work differently.

ParameterDescription
stepxHorizontal shift amount
stepyVertical shift amount

sym_bg2

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

Type: 2D
Author: Jesus Sosa
Date: 5 May 2021

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

Sym_bg2, sym_bg5, sym_ng2, and sym_ng7 do the same thing, except the parameters work differently.

ParameterDescription
stepxHorizontal shift amount
stepyVertical shift amount

sym_bg3

Make two copies of the flame, the original and a 180° rotation.

Type: 2D
Author: Jesus Sosa
Date: 5 May 2021

To make the copies overlap, set stepx=-2 and stepy=-1. Then adjust the parameters to achieve the desired positioning.

ParameterDescription
stepxHorizontal shift amount
stepyVertical shift amount

sym_bg4

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

Type: 2D
Author: Jesus Sosa
Date: 5 May 2021

To make the copies overlap, set stepx=-2 and stepy=-1. Then adjust the parameters to achieve the desired positioning.

ParameterDescription
stepxHorizontal shift amount
stepyVertical shift amount

sym_bg5

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

Type: 2D
Author: Jesus Sosa
Date: 5 May 2021

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

Sym_bg2, sym_bg5, sym_ng2, and sym_ng7 do the same thing, except the parameters work differently.

ParameterDescription
stepxHorizontal shift amount
stepyVertical shift amount

sym_bg6

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

Type: 2D
Author: Jesus Sosa
Date: 5 May 2021

To make the copies overlap horizontally, set stepx=-2. Set stepy=0 to maximize the vertical overlap, though it won’t be complete (use sym_bg7 if this is needed). Then adjust the parameters to achieve the desired positioning.

Sym_bg6, sym_bg7, sym_ng4, sym_ng5, and sym_ng9 do the same thing, except the parameters work differently (sym_ng4 is the most flexible).

ParameterDescription
stepxHorizontal shift amount
stepyVertical shift amount

sym_bg7

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

Type: 2D
Author: Jesus Sosa
Date: 5 May 2021

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

Sym_bg6, sym_bg7, sym_ng4, sym_ng5, and sym_ng9 do the same thing, except the parameters work differently (sym_ng4 is the most flexible).

ParameterDescription
stepxHorizontal shift amount
stepyVertical shift amount

sym_ng1

Make two identical copies of the flame.

Type: 2D
Author: Jesus Sosa
Date: 5 May 2021

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

Sym_bg1 and sym_ng1 do the same thing, except the parameters work differently.

ParameterDescription
stepxHorizontal shift amount
stepyVertical shift amount

sym_ng2

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

Type: 2D
Author: Jesus Sosa
Date: 5 May 2021

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

Sym_bg2, sym_bg5, sym_ng2, and sym_ng7 do the same thing, except the parameters work differently.

ParameterDescription
stepxHorizontal shift amount
stepyVertical shift amount

sym_ng3

Make two copies of the flame, the original and a 180° rotation.

Type: 2D
Author: Jesus Sosa
Date: 5 May 2021

To make the copies overlap, set sepx=0, sepy=0, and step=0. Then adjust the parameters to achieve the desired positioning.

Sym_bg3 and sym_ng3 do the same thing, except the parameters are different.

ParameterDescription
sepxHorizontal shift amount
sepyVertical shift amount
stepDiagonal shift amount

sym_ng4

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

Type: 2D
Author: Jesus Sosa
Date: 5 May 2021

To make the copies overlap, set sepx=-2, sepy=1, stepx=-2, and stepy=-1. Then adjust the parameters to achieve the desired positioning.

Sym_bg6, sym_bg7, sym_ng4, sym_ng5, and sym_ng9 do the same thing, except the parameters work differently (sym_ng4 is the most flexible).

ParameterDescription
sepxHorizontal shift amount for the vertical reflections
sepyVertical shift amount for the horizontal reflections
stepxHorizontal shift amount for the rotations
stepyVertical shift amount for the rotations

sym_ng5

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

Type: 2D
Author: Jesus Sosa
Date: 5 May 2021

To make the copies overlap, set sepx=-1, sepy=0, and stepx=-2. Then adjust the parameters to achieve the desired positioning.

Sym_bg6, sym_bg7, sym_ng4, sym_ng5, and sym_ng9 do the same thing, except the parameters work differently (sym_ng4 is the most flexible).

ParameterDescription
sepxHorizontal shift amount for the vertical reflections
sepyVertical shift amount for the horizontal reflections
stepxHorizontal shift amount for the rotations

sym_ng6

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

Type: 2D
Author: Jesus Sosa
Date: 5 May 2021

To make the copies overlap, set sepy=0, stepx=0, and stepy=0. Then adjust the parameters to achieve the desired positioning.

ParameterDescription
sepyVertical shift amount for the identical copies
stepxHorizontal shift amount for the reflected copies
stepyVertical shift amount for the reflected copies

sym_ng7

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

Type: 2D
Author: Jesus Sosa
Date: 5 May 2021

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

Sym_bg2, sym_bg5, sym_ng2, and sym_ng7 do the same thing, except the parameters work differently.

ParameterDescription
stepxHorizontal shift amount
stepyVertical shift amount

sym_ng8

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

Type: 2D
Author: Jesus Sosa
Date: 5 May 2021

To make the copies overlap, set sepx=2, sepy=0, skewx=0, and skewy=0. Then adjust the parameters to achieve the desired positioning.

Sym_ng8 is like sym_bg6, sym_bg7, sym_ng4, sym_ng5, and sym_ng9 when skewx and skewy are 0. Change skewx and skewy to separate all eight copies.

ParameterDescription
sepxHorizontal shift amount for the identical copies
sepyVertical shift amount for the identical copies
skewxHorizontal shift amount for the other copies
skewyVertical shift amount for the other copies

sym_ng9

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

Type: 2D
Author: Jesus Sosa
Date: 5 May 2021

To make the copies overlap, set sepx=0 and sepy=0. Then adjust the parameters to achieve the desired positioning.

Sym_bg6, sym_bg7, sym_ng4, sym_ng5, and sym_ng9 do the same thing, except the parameters work differently (sym_ng4 is the most flexible).

ParameterDescription
sepxHorizontal shift amount
sepyVertical shift amount

sym_ng10

Make four copies of the flame at 90° angles from each other.

Type: 2D
Author: Jesus Sosa
Date: 5 May 2021

To make the copies overlap, set space=0, spacex=0 and spacey=0. Then adjust the parameters to achieve the desired positioning.

ParameterDescription
spaceRadial shift amount
spacexHorizontal shift amount
spaceyVertical shift amount

sym_ng11

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

Type: 2D
Author: Jesus Sosa
Date: 5 May 2021

To make the copies overlap, set all parameters to 0. Then adjust the parameters to achieve the desired positioning.

Sym_ng11 and sym_ng12 do the same thing, except the parameters work differently (sym_ng11 is the most flexible).

ParameterDescription
spaceRadial shift amount
spacexHorizontal shift amount
spaceyVertical shift amount
stepxHorizontal spacing between the rotations and their reflections
stepyVertical spacing between the rotations and their reflections

sym_ng12

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

Type: 2D
Author: Jesus Sosa
Date: 5 May 2021

To make the copies overlap, set all parameters to 0. Then adjust the parameters to achieve the desired positioning.

Sym_ng11 and sym_ng12 do the same thing, except the parameters work differently (sym_ng11 is the most flexible).

ParameterDescription
spaceRadial shift amount
spacexHorizontal shift amount
spaceyVertical shift amount

sym_ng13

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

Type: 2D
Author: Jesus Sosa
Date: 5 May 2021

To make the copies overlap, set all parameters to 0. Then adjust the parameters to achieve the desired positioning.

ParameterDescription
radiusRadial shift amount
stepxHorizontal shift amount
stepyVertical shift amount

sym_ng14

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

Type: 2D
Author: Jesus Sosa
Date: 5 May 2021

To make the copies overlap, set all parameters to 0. Then adjust the parameters to achieve the desired positioning.

ParameterDescription
radiusRadial shift amount
stepxHorizontal shift amount
stepyVertical shift amount

sym_ng15

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

Type: 2D
Author: Jesus Sosa
Date: 5 May 2021

To make the copies overlap, set all parameters to 0. Then adjust the parameters to achieve the desired positioning.

Sym_ng14 and sym_ng15 are similar, but rotated 30° from each other. Each makes three “arms”; sym_ng14 has one arm horizontal and sym_ng15 has one arm vertical.

ParameterDescription
radiusRadial shift amount
stepxHorizontal shift amount
stepyVertical shift amount

sym_ng16

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

Type: 2D
Author: Jesus Sosa
Date: 5 May 2021

To make the copies overlap, set all parameters to 0. Then adjust the parameters to achieve the desired positioning.

ParameterDescription
radiusRadial shift amount
stepxHorizontal shift amount
stepyVertical shift amount

sym_ng17

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

Type: 2D
Author: Jesus Sosa
Date: 5 May 2021

To make the copies overlap, set all parameters to 0. Then adjust the parameters to achieve the desired positioning.

ParameterDescription
radiusRadial shift amount
stepxHorizontal shift amount
stepyVertical shift 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.
Creative Commons License
This work is licensed under a Creative Commons Attribution-ShareAlike 4.0 International License.

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