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FracTeX

FracTeX

This package provides commands to visualize various types of fractals using PGFPlots and LuaTeX.

Supported Fractals:

  • Mandelbrot Set
  • Julia Set
  • Barnsley Fern (IFS)
  • Burning Ship Fractal
  • Newton Fractal
  • Phoenix Fractal
  • Tricorn Fractal
  • Buffalo Fractal
  • Sierpiński Triangle
  • Lyapunov Fractal
  • Magnet Fractal
  • Multibrot Set
  • Gingerbreadman Map

Requirements

This package requires pgfplots, luacode and xkeyva. Additionally, since Lua is used for coordinate calculations, LuaLaTeX must be used.

Installation

To install this package, you can clone the repository from GitHub:

git clone https://github.com/rice8y/FracTeX.git

Windows

On Windows, you can simply run the following command to install the package:

install

Linux/macOS

For Linux and macOS, you can use the provided shell script to install the package:

./install.sh

Usage

Mandelbrot Set

\MandelbrotSet
% options: \MandelbrotSet[xmin=-2,xmax=1,ymin=-1.5,ymax=1.5,dx=0.02,dy=0.02,max_iter=100,cmap=jet]

Parameters:

  • xmin/xmax: X-axis range (default: -2/1)
  • ymin/ymax: Y-axis range (default: -1.5/1.5)
  • dx/dy: Resolution parameters (default: 0.02/0.02)
  • max_iter: Iteration limit (default: 100)
  • cmap: Color scheme (default: jet)

Julia Set

\JuliaSet
% options: \JuliaSet[xmin=-2,xmax=2,ymin=-1.5,ymax=1.5,dx=0.02,dy=0.02,c_re=-0.8,c_im=0.156,max_iter=100,cmap=jet]

Parameters:

  • xmin/xmax: X-axis range (default: -2/2)
  • ymin/ymax: Y-axis range (default: -1.5/1.5)
  • dx/dy: Resolution parameters (default: 0.02/0.02)
  • c_re/c_im: Complex constant components (default: -0.8/0.156)
  • max_iter: Iteration limit (default: 100)
  • cmap: Color scheme (default: jet)

Barnsley Fern

\BarnsleyFern
% options: \BarnsleyFern[num_points=50000,color=green]

Parameters:

  • num_points: Number of generated points (default: 50000)
  • color: Base color (default: green)

Burning Ship Fractal

\BurningShipFractal
% options: \BurningShipFractal[xmin=-2,xmax=1.5,ymin=-2,ymax=1,dx=0.02,dy=0.02,max_iter=100,cmap=jet]

Parameters:

  • xmin/xmax: X-axis range (default: -2/1.5)
  • ymin/ymax: Y-axis range (default: -2/1)
  • dx/dy: Resolution parameters (default: 0.02/0.02)
  • max_iter: Iteration limit (default: 100)
  • cmap: Color scheme (default: jet)

Newton Fractal

\NewtonFractal
% options: \NewtonFractal[xmin=-1.5,xmax=1.5,ymin=-1.5,ymax=1.5,dx=0.02,dy=0.02,max_iter=20,cmap=jet]

Parameters:

  • xmin/xmax: X-axis range (default: -1.5/1.5)
  • ymin/ymax: Y-axis range (default: -1.5/1.5)
  • dx/dy: Resolution parameters (default: 0.02/0.02)
  • max_iter: Iteration limit (default: 20)
  • cmap: Color scheme (default: jet)

Phoenix Fractal

\PhoenixFractal
% options: \PhoenixFractal[xmin=-1.5,xmax=1.5,ymin=-1.5,ymax=1.5,dx=0.02,dy=0.02,P=0.3,max_iter=50,cmap=jet]

Parameters:

  • xmin/xmax: X-axis range (default: -1.5/1.5)
  • ymin/ymax: Y-axis range (default: -1.5/1.5)
  • dx/dy: Resolution parameters (default: 0.02/0.02)
  • P: Feedback parameter (default: 0.3)
  • max_iter: Iteration limit (default: 50)
  • cmap: Color scheme (default: jet)

Tricorn Fractal

\TricornFractal
% options: \TricornFractal[xmin=-2,xmax=1,ymin=-1.5,ymax=1.5,dx=0.02,dy=0.02,max_iter=100,cmap=jet]

Parameters:

  • xmin/xmax: X-axis range (default: -2/1)
  • ymin/ymax: Y-axis range (default: -1.5/1.5)
  • dx/dy: Resolution parameters (default: 0.02/0.02)
  • max_iter: Iteration limit (default: 100)
  • cmap: Color scheme (default: jet)

Buffalo Fractal

\BuffaloFractal
% options: \BuffaloFractal[xmin=-2,xmax=1,ymin=-1.5,ymax=1.5,dx=0.02,dy=0.02,max_iter=100,cmap=jet]

Parameters:

  • xmin/xmax: X-axis range (default: -2/1)
  • ymin/ymax: Y-axis range (default: -1.5/1.5)
  • dx/dy: Resolution parameters (default: 0.02/0.02)
  • max_iter: Iteration limit (default: 100)
  • cmap: Color scheme (default: jet)

Sierpinski Triangle

\SierpinskiTriangle
% options: \SierpinskiTriangle[num_points=50000,color=blue]

Parameters:

  • num_points: Points count (default: 50000)
  • color: Base color (default: blue)

Lyapunov Fractal

\LyapunovFractal
% options: \LyapunovFractal[amin=2.4,amax=3.6,bmin=2.4,bmax=3.6,da=0.01,db=0.01, max_iter=100,cmap=hot]

Parameters:

  • amin/amax: Parameter a range (default: 2.4/3.6)
  • bmin/bmax: Parameter b range (default: 2.4/3.6)
  • da/db: Resolution parameters (default: 0.01/0.01)
  • max_iter: Iteration limit (default: 100)
  • cmap: Color scheme (default: hot)

Magnet Fractal

\MagnetFractal
% options: \MagnetFractal[xmin=-2,xmax=2,ymin=-2,ymax=2,dx=0.02,dy=0.02,max_iter=100,cmap=jet]

Parameters:

  • xmin/xmax: X-axis range (default: -2/2)
  • ymin/ymax: Y-axis range (default: -2/2)
  • dx/dy: Resolution parameters (default: 0.02/0.02)
  • max_iter: Iteration limit (default: 100)
  • cmap: Color scheme (default: jet)

Multibrot Set

\MultibrotSet
% options: \MultibrotSet[xmin=-2,xmax=2,ymin=-2,ymax=2,dx=0.02,dy=0.02,d=3,max_iter=100,cmap=jet]

Parameters:

  • xmin/xmax: X-axis range (default: -2/2)
  • ymin/ymax: Y-axis range (default: -2/2)
  • dx/dy: Resolution parameters (default: 0.02/0.02)
  • d: Power parameter (default: 3)
  • max_iter: Iteration limit (default: 100)
  • cmap: Color scheme (default: jet)

Gingerbreadman Map

\GingerbreadmanMap
% options: \GingerbreadmanMap[num_points=50000, color=red]

Parameters:

  • num_points: Points count (default: 50000)
  • color: Base color (default: red)

License

This package is distributed under the BSD 2-Clause License. See LICENSE.