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 40,000 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
- 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
- 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
- Henon Phase Diagrams
- Rossler
- Lorenz
- Test Pattern (Square)
- Test Pattern (Round)
Alternate Values
- Orbit Point
- Continuous Potential
- Exponential Smoothing
- Exponential Smoothing (Optimized)
- Exponential Smoothing (DistanceMetric)
- Distance Estimator
- Triangle Inequality Average
- Biomorph
- Trapped Average Angle
- Geometric Pattern
- Perlin Noise
- Markus-Lyapunov
Orbit Traps
- Circle
- Line
- Polygon
- Shape
- Cross
- Crossed Lines
- Cassinian Curve
- Circular Vine
- Borromean Rings
- Tangent Circles
- String Art
- Ornament
- Sectors
- Triangles
- Star Polygon
- Composite Shape
- Spiral
- Swirl
- Flower
- Rose
- Super Ellipse
- Geometric Pattern
- Sound Ornament
- Shapes
- Squares
- Circle Inversion
- Circle Inversion 2
- Apollonian Gasket
- 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 - Average Value
- Gradient Map - Color Blend
- Gradient Map - Trap Overlay 1
- Gradient Map - Trap Overlay 2
- Gradient Map - Complex Analysis
- Gradient Map - Biomorph
- Pattern Map - Texture
- Pattern Map - Geometric Design
- Pattern Map - Perlin Noise
- Pattern Map - Perlin Noise (Pixel)
- Direct Color Map - RGB
- Direct Color Map - RGB Blend
- Markus-Lyapunov
Classic Master Controllers
- Pass Thru
- Series
- Inside/Outside
- Switch
- Transition
- Blend
Orbit Trap Controllers
- Gradient Map - Value
- 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
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
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)
- Circle Inversion
- Double Inversion
- Triangle Metric Point
- Droste Effect - Circles
- 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
- Z Rotate
- Z Rotate Arg(z)
- Z Reflect
- Z Shear
- Z Bend
- Z Shift
- Z Previous
- Affine 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
- Poincare Disk
- Composite Transform
- Weighted Average
- Weighted Lookup
- Composite Function Chain
- Composite Triangle Function
- Continued Fraction
- Circle Inversion
- Double Circle Inversion
- Triangle Inversion
- Triangle Point
- Conchoid
- Strophoid
- Spiral
- Swirl
- Cycloid
- Double Cycloid
- Flame Variation
- Shape Value
- Shape Transformation
- Oblique
- Anti-Mercator
- Stereographic Projection
- Azimuthal Equidistant
- Circle Limit
- Orbital Symmetry
- Orbital Scaling
- Orbital Spiral
- Kaleidoscope - Slices
- Kaleidoscope - Squares
- Kaleidoscope - Triangles
- Droste Effect - Circles
- Triangle Metric Function
- Triangle Vector Function
- Triangle Point Function