Built-in Programs

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Built-in Fractal Programs

The Fractal Science Kit fractal generator supports hundreds of built-in equations, transformations, orbit traps, and color controllers, allow the casual user to produce stunning fractal images while providing the experienced fractal developer a rich set of illustrative examples on which to build his/her own programs. The more than 60,000 lines of source code for the built-in fractal programs and the built-in macros (inline functions/methods) are accessible via the Program Browser and Macro Editor, respectively.

There are 12 different Program Types. While this may seem overwhelming at first glance, be assured that each type is responsible for performing a small, well defined task, which can be handled by the default configuration until you choose to explore that area of the application. What's more, because of this partitioning, there are countless opportunities for combining programs in new and unusual ways.

Below find a list of the build-in fractal programs categorized by type. This document does not describe the programs, but simply lists the programs of each type for reference. The fractal programs are described in the comment section at the beginning of each program. Please refer to the source code for details.

Fractal Equations

  • Mandelbrot
  • Mandelbrot Power
  • Mandelbar
  • Mandelbar Power
  • Cubic 1
  • Cubic 2
  • Lambda
  • Phoenix
  • Phoenix Map
  • Peterson
  • Quartet
  • Tetrate
  • Super Tetrate
  • Newton 1
  • Newton 2
  • Newton 3
  • Newton 4
  • Newton 5
  • Newton 6
  • Newton 7
  • Newton 8
  • Newton 9
  • Newton 10
  • Newton 11
  • Newton 12
  • Nova 1
  • Nova 2
  • Nova 3
  • Nova 4
  • Nova 5
  • Nova 6
  • Cactus
  • Tails
  • The Burning Ship
  • The Bird of Prey
  • Barnsley 1
  • Barnsley 2
  • Barnsley 3
  • Sierpinski
  • Sierpinski Web
  • Devaney 1
  • Devaney 2
  • Tricorn
  • Carlson - Pokorny 1
  • Carlson - Pokorny 2
  • Carlson - Example 1
  • Carlson - Example 2
  • Carlson - Example 3
  • Carlson - Newton 1
  • Carlson - Newton 2
  • Carlson - Newton 3
  • Carlson - Celtic
  • Carlson - Continued Fraction Function
  • Fractal Domains - Wholly Holey
  • Fractal Domains - Trefoil
  • Fractal Domains - Convergence
  • Fractal Domains - Circle of Chaos
  • Fractal Domains - Roots of Chaos
  • Fractal Domains - Dazzle
  • Fractal Domains - Birthday Blast
  • Fractal Domains - Focus
  • Fractal Domains - Doubled Fours
  • Fractal Domains - Phalanx
  • Fractal Domains - Spiral Lattice
  • Fractal Domains - Venus Flytrap
  • Convergent Map 1
  • Convergent Map 2
  • Convergent Map 3
  • Convergent Map 4
  • Convergent Map 5
  • Convergent Map 6
  • Convergent Map 7
  • Convergent Map 8
  • Convergent Map 9
  • Convergent Map 10
  • Convergent Map 11
  • Convergent Map 12
  • Convergent Map 13
  • Convergent Map 14
  • Magnet 1
  • Magnet 2
  • Biomorph 1
  • Biomorph 2
  • Biomorph 3
  • Biomorph 4
  • Biomorph 5
  • Biomorph Tree
  • Manowar
  • Spider
  • Fractal Moon
  • Szegedi Butterfly
  • Thorn Fractal
  • Volterra-Lotka
  • Sqrt
  • Fractovia
  • NanoGeometry 1
  • NanoGeometry 2
  • NanoGeometry 3
  • NanoGeometry 4
  • NanoGeometry 5
  • NanoGeometry 6
  • NanoGeometry 7
  • Newton Basins 1
  • Newton Basins 2
  • Newton Basins 3
  • Bee
  • Pinwheels
  • Volcano
  • Composite Function
  • Composite Function Expression
  • Composite Function Chain
  • Newton Composite Function
  • Julia Map 1
  • Julia Map 2
  • Julia Map 3
  • Julia Map 4
  • Julia Map 5
  • Julia Map 6
  • Julia Map 7
  • Julia Map 8
  • Julia Pattern Map
  • Polynomial 1
  • Polynomial 2
  • Polynomial Quotient
  • Poly 3a
  • Poly 3b
  • Poly 3c
  • Poly 4a
  • Poly 4b
  • Poly 4c
  • Poly 4d
  • Poly 5a
  • Poly 5b
  • Poly 5c
  • Poly 6a
  • Poly 6b
  • Poly 6c
  • Newton Poly 4a
  • Newton Poly 4b
  • Newton Poly 4c
  • Newton Poly 5a
  • Newton Poly 5b
  • Newton Poly 5c
  • Newton Poly 5d
  • Newton Poly 6a
  • Newton Poly 6b
  • Newton Poly 6c
  • Newton Poly 7a
  • Newton Poly 7b
  • Newton Poly 7c
  • Trig 1
  • Trig 2
  • Trig 3
  • Trig 4
  • Trig 5
  • Trig 6
  • Trig 7
  • Trig 8
  • Trig 9
  • Trig 10
  • Trig 11
  • Trig 12
  • Trig 13
  • Trig 14
  • Trig 15
  • Trig 16
  • Trig 17
  • Exp 1
  • Exp 2
  • Exp 3
  • Exp 4
  • Exp 5
  • Exp 6
  • Exp 7
  • Exp 8
  • Exp 9
  • Exp 10
  • Exp 11
  • Exp 12
  • Exp 13
  • Exp 14
  • Exp 15
  • Exp 16
  • Exp 17
  • Z Power 1
  • Z Power 2
  • Z Power 3
  • Poisson Z
  • Airfoil 1
  • Airfoil 2
  • Airfoil 3
  • Pixel

Orbital Equations

  • Sierpinski Triangle
  • Sierpinski Relatives
  • Sierpinski N-gons
  • Sierpinski N-gons (Variations)
  • Koch Snowflake
  • Koch Snowflake (Variations)
  • Apollonian Gasket
  • Apollonian Gasket (Variations)
  • Circle Inversion
  • Circle Inversion 2
  • Kleinian Group - Examples
  • Kleinian Group - Variations
  • Flame (2 Transforms)
  • Flame (4 Transforms)
  • Flame (6 Transforms)
  • Flame (8 Transforms)
  • Mobius Dragon IFS
  • Mobius Patterns
  • Grand Julian IFS
  • Elliptic Splits IFS
  • Dragons
  • Dimers
  • Rep-4 Tile
  • Rep-4 Equilateral Triangle
  • Rep-4 Triangle
  • Rep-4 Parallelogram
  • Rep-9 Tile
  • Rep-9 Equilateral Triangle
  • Rep-9 Triangle
  • Rep-9 Parallelogram
  • IFS Examples - Chaos and Fractals
  • IFS Examples - Yale
  • IFS File Processor
  • IFS (Search)
  • Quadratic Attractors
  • Quadratic Attractors (Search)
  • Cubic Attractors
  • Cubic Attractors (Search)
  • Clifford Attractors
  • Peter de Jong Attractors
  • Pickover Attractors
  • Symmetric Icon - Standard Formula
  • Symmetric Icon - Standard Formula (Search)
  • Symmetric Icon - Non-Polynomial Term
  • Symmetric Icon - Non-Polynomial Term (Search)
  • Symmetric Icon - Variations
  • Symmetric Icon - Variations (Search)
  • Symmetric Attractors
  • Symmetric Attractors (Search)
  • Frieze Group
  • Frieze Group (Search)
  • Wallpaper Group - Square Lattice
  • Wallpaper Group - Square Lattice (Search)
  • Hyperbolic Attractors
  • Inverse Julia
  • Mira Variations
  • Gingerbread Man
  • Hopalong
  • Ikeda
  • Henon
  • Rossler
  • Lorenz
  • Test Pattern (Square)
  • Test Pattern (Round)

Alternate Values

  • Orbit Point
  • Continuous Potential
  • Exponential Smoothing
  • Exponential Smoothing (Optimized)
  • Exponential Smoothing (Delta)
  • Exponential Smoothing (Triangle Metric Value)
  • Blended Value
  • Statistics
  • Minimum Value/Delta
  • Minimum Shape
  • Average Angle
  • Distance Estimator
  • Triangle Inequality Average
  • Surface Normal Styles
  • Biomorph
  • Trapped Average Angle
  • Trapped Index/Delta Sum
  • Geometric Pattern
  • Perlin Noise
  • Markus-Lyapunov

Orbit Traps

  • Circle
  • Line
  • Polygon
  • General Polygon
  • Spinning Polygon
  • Shape
  • Tangent Shapes
  • Sphere
  • Patterned Sphere
  • Solid Polygon
  • Solid General Polygon
  • Patterned Polygon
  • Patterned General Polygon
  • Epicycloid Polygon
  • Hypocycloid Polygon
  • Circumscribed Disk
  • Cross
  • Crossed Lines
  • Image
  • Transformation
  • Cassinian Curve
  • Limacon
  • Lemniscate
  • Folium
  • Cycloid of Ceva
  • Heart
  • Set of Polygons
  • Ring of Polygons
  • Hexagon of Triangles
  • Circular Vine
  • Celtic Knot
  • Borromean Rings
  • Tangent Circles
  • Steiner Chain
  • Rep-4 Tile
  • Rep-4 Tile Patterned Polygon
  • Rep-4 Tile Patterned General Polygon
  • Rep-9 Tile
  • Rep-9 Tile Patterned Polygon
  • Rep-9 Tile Patterned General Polygon
  • Pythagorean Tree
  • Tiling
  • Polygon Motif
  • Star of David
  • String of Beads
  • Wheel
  • Limacon Net
  • Lemniscate Net
  • Nephroid Net
  • Epitrochoid Net
  • Hypotrochoid Net
  • Polygon Net
  • Polygon Whirl
  • Circle Web
  • String Art
  • Ornament
  • Sectors
  • Triangles
  • Star Polygon
  • Faceted Polygon
  • Composite Shape
  • Spiral
  • Daisy
  • Swirl
  • Flower
  • Rose
  • Maurer Rose
  • Epitrochoid Rose
  • Farris Wheels
  • Farris Wheels Net
  • Harmonograph
  • Super Ellipse
  • Geometric Pattern
  • Sound Ornament
  • Shapes
  • Squares
  • Circle Inversion
  • Circle Inversion 2
  • Ford Circles
  • Apollonian Gasket
  • Hyperbolic Tiling
  • Inversion Group
  • Elliptic Circles
  • Hyperbolic Circles
  • Parabolic Circles
  • Schottky Group
  • Kleinian Group
  • Unit Circle Group
  • Complex Grid
  • Circular Grid
  • Hexagon Grid
  • Shape Grid
  • Apollonius Grid
  • Parabolic Grid

Classic Controllers

  • Gradient Map - Value
  • Gradient Map - Inside/Outside
  • Gradient Map - Binary Decomposition
  • Gradient Map - Atan 1
  • Gradient Map - Atan 2
  • Gradient Map - Atan 1 (Alternate Mapping 1)
  • Gradient Map - Atan 2 (Alternate Mapping 1)
  • Gradient Map - Newton
  • Gradient Map - Angle Relief (Smooth Angle)
  • Gradient Map - Angle Relief (x^2)
  • Gradient Map - Angle Relief (y^2)
  • Gradient Map - Value/Overlay
  • Gradient Map - Value/Overlay (Smoothed)
  • Gradient Map - Value/Overlay (Shift)
  • Gradient Map - Value/Overlay (Trap)
  • Gradient Map - Split Value
  • Gradient Map - Average Value
  • Gradient Map - Color Blend
  • Gradient Map - Trap Overlay 1
  • Gradient Map - Trap Overlay 2
  • Gradient Map - Complex Analysis
  • Gradient Map - Biomorph
  • Gradient Map - Stripes
  • Gradient Map - Stripes (Binary Decomposition)
  • Pattern Map - Texture
  • Pattern Map - Texture (Planar)
  • Pattern Map - Geometric Design
  • Pattern Map - Perlin Noise
  • Pattern Map - Perlin Noise (Planar)
  • Pattern Map - Brushed Metal
  • Pattern Map - Stone/Metal/Wood
  • Pattern Map - Stone/Metal/Wood (Binary Decomposition)
  • Pattern Map - Stone/Metal/Wood (Planar)
  • Pattern Map - Stripes
  • Pattern Map - Stripes (Binary Decomposition)
  • Pattern Map - Tile
  • Pattern Map - Tile (Binary Decomposition)
  • Pattern Map - Texture Tile
  • Pattern Map - Texture Tile (Binary Decomposition)
  • Pattern Map - Voronoi
  • Pattern Map - Voronoi (Binary Decomposition)
  • Pattern Map - Voronoi (Planar)
  • Color Map - Yin and Yang
  • Direct Color Map - RGB
  • Direct Color Map - RGB Blend
  • Markus-Lyapunov

Classic Master Controllers

  • Pass Thru
  • Series
  • Inside/Outside
  • Switch
  • Trap Switch
  • Transition
  • Dwell Transition
  • Dwell Transition (Binary Decomposition)
  • Blend

Orbit Trap Controllers

  • Gradient Map - Value
  • Gradient Map - Average Value
  • Gradient Map - Color Blend
  • Gradient Map - Value Sum
  • Gradient Map - Striped Values
  • Gradient Map - Carlson Ramps
  • Gradient Map - Dwell/Index
  • Color Map - Dwell/Index
  • Pattern Map - Texture
  • Pattern Map - Geometric Design 1
  • Pattern Map - Geometric Design 2
  • Pattern Map - Sound Ornament
  • Pattern Map - Perlin Noise
  • Pattern Map - Brushed Metal
  • Pattern Map - Stone/Metal/Wood (Planar Map)
  • Pattern Map - Stone/Metal/Wood (Curve Map)
  • Pattern Map - Stone/Metal/Wood (Solid Map)
  • Pattern Map - Stripes (Planar Map)
  • Pattern Map - Stripes (Curve Map)
  • Pattern Map - Stripes (Solid Map)
  • Pattern Map - Tile (Planar Map)
  • Pattern Map - Tile (Curve Map)
  • Pattern Map - Tile (Solid Map)
  • Pattern Map - Voronoi (Planar Map)
  • Pattern Map - Voronoi Tile (Planar Map)
  • Pattern Map - Symmetric Pattern (Solid Map)
  • Image Map

Orbit Trap Master Controllers

  • Pass Thru
  • Series
  • Index Map
  • Switch
  • Blend

Orbital Controllers

  • Gradient Map - Value
  • Gradient Map - Color Blend
  • Color Map - Index
  • Direct Color Map - RGB
  • Direct Color Map - RGB Blend

Orbital Master Controllers

  • Pass Thru
  • Alpha Map

Symmetry Transformations

  • Identity
  • Reflection
  • Rotation
  • Scaling
  • Inversion
  • Spiral Symmetry
  • Rosette Symmetry Group
  • Plane Symmetry Groups - Square Lattice
  • Plane Symmetry Groups - Hexagonal Lattice
  • Translation (1-Dimensional)
  • Translation (2-Dimensional)
  • Hexagon Grid
  • IFS (4 Transforms)
  • Golden Rectangle
  • Golden Triangle
  • Rectangular Spiral
  • Rep-4 Tile
  • Plane Tiling
  • Polar Tiling
  • Logarithmic Spiral Tiling
  • Hyperbolic Tiling
  • Hyperbolic Tiling - Orbital
  • Circle Inversion
  • Double Inversion
  • Triangle Metric Point
  • Complex Functions
  • Complex Transformations
  • Transformation Powers
  • Transformation Shift - Rotate
  • Transformation Shift - Linear Path
  • Transformation Shift - Circular Path
  • Transformation Shift - Reflected Sectors
  • Transformation Shift - Mobius Interpolation

Transformations

  • Identity
  • Composite Function
  • Combined Functions
  • Composite Function (Symmetric)
  • Combined Functions (Symmetric)
  • Z Rotate
  • Z Rotate Arg(z)
  • Z Reflect
  • Z Reflect (Conditional)
  • Z Shear
  • Z Bend
  • Z Shift
  • Z Previous
  • Affine Transformation
  • Mobius Transformation
  • Mobius Transformation - Elliptic
  • Mobius Transformation - Hyperbolic
  • Mobius Transformation - Loxodromic
  • Mobius Transformation - Parabolic
  • Disc Automorphism - Elliptic
  • Disc Automorphism - Hyperbolic
  • Disc Automorphism - Parabolic
  • Disc Automorphism - General
  • Half-Plane to Disk
  • Circle To Circle
  • Poincare Disk
  • Mobius Group
  • Julia
  • Julia (Enhanced)
  • Disk
  • Plane To Strip
  • Plane To Disk
  • Disk To Strip
  • Strip To Ring
  • Hole
  • Reflecting Pool
  • Composite Transform
  • Conditional Transform
  • Weighted Average
  • Weighted Lookup
  • Composite Function Chain
  • Composite Triangle Function
  • Continued Fraction
  • Spherical
  • Circle Inversion
  • Circle Inversion (Conditional)
  • Circle Inversion (Ring)
  • Double Circle Inversion
  • Tangent Circles Inversion
  • Triangle Inversion
  • Triangle Point
  • Conchoid
  • Strophoid
  • Spiral
  • Swirl
  • Cycloid
  • Double Cycloid
  • Alternate Cycloid
  • Flame Transformation
  • Polygon (Regular)
  • Polygon (Star)
  • Polygon (Gear)
  • Shape Value
  • Shape Blend
  • Shape Transformation
  • Oblique
  • Perspective
  • Anti-Mercator
  • Stereographic Projection
  • Azimuthal Equidistant
  • Cylindrical Projection (Stereographic)
  • Cylindrical Projection (Azimuthal Equidistant)
  • Circle Limit
  • Strip Limit
  • Rectangle Limit
  • Orbital Symmetry
  • Orbital Reflection
  • Orbital Scaling
  • Orbital Translation (1-Dimensional)
  • Orbital Translation (2-Dimensional)
  • Orbital Spiral
  • Orbital Daisy
  • Orbital Circle Inversion
  • Orbital Density Adjustment (Circle)
  • Orbital Density Adjustment (Waves)
  • Spheres
  • Kaleidoscope - Slices
  • Kaleidoscope - Squares
  • Kaleidoscope - Triangles
  • Golden Rectangle
  • Golden Triangle
  • Rectangular Spiral
  • Rep-4 Tile
  • Polar Tiling
  • Logarithmic Spiral Tiling
  • Hyperbolic Tiling
  • Hyperbolic Tiling - Orbital
  • Hyperbolic Tile
  • Sierpinski Triangle
  • Droste Effect - Circles
  • Droste Effect - Orbital
  • Triangle Metric Function
  • Triangle Vector Function
  • Triangle Point Function
  • Wrap
  • Clip
  • Clip (Half-Plane)
  • Clip (Polygon)

 

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