leaf_chaos


leaf_chaos, a Fortran90 code which applies a randomized linear map to a starting point to compute a dot-plot image of a leaf.

Licensing:

The information on this web page is distributed under the MIT license.

Languages:

leaf_chaos is available in a C version and a C++ version and a Fortran90 version and a MATLAB version and an Octave version and a Python version.

Related Data and Programs:

leaf_chaos_test

cross_chaos, a Fortran90 code which creates a dot-plot of a cross by repeatedly applying a randomized linear transformation to a starting point.

dragon_chaos, a Fortran90 code which creates a dot-plot of a dragon by repeatedly applying a randomized linear transformation to a starting point.

fern_chaos, a Fortran90 code which applies a randomized linear map to a starting point to compute a dot-plot of the Barnsley fractal fern.

levy_dragon_chaos, a Fortran90 code which creates a dot-plot of the Levy dragon by repeatedly applying a randomized linear transformation to a starting point.

menger_sponge_chaos, a Fortran90 code which creates a dot-plot of the 3D Menger sponge by repeatedly applying a randomized linear transformation to a starting point.

sierpinski_carpet_chaos, a Fortran90 code which creates a dot-plot of the Sierpinski carpet by repeatedly applying a randomized linear transformation to a starting point.

sierpinski_triangle_chaos, a Fortran90 code which creates a dot-plot of the Sierpinski triangle by repeatedly applying a randomized linear transformation to a starting point.

tree_chaos, a Fortran90 code which creates a dot-plot of a tree by repeatedly applying a randomized linear transformation to a starting point.

Reference:

  1. Scott Bailey, Theodore Kim, Robert Strichartz,
    Inside the Levy dragon,
    American Mathematical Monthly,
    Volume 109, Number 8, October 2002, pages 689-703.
  2. Michael Barnsley, Alan Sloan,
    A Better Way to Compress Images,
    Byte Magazine,
    Volume 13, Number 1, January 1988, pages 215-224.
  3. Michael Barnsley,
    Fractals Everywhere,
    Academic Press, 1988,
    ISBN: 0120790696,
    LC: QA614.86.B37.
  4. Michael Barnsley, Lyman Hurd,
    Fractal Image Compression,
    Peters, 1993,
    ISBN: 1568810008,
    LC: TA1632.B353
  5. Alexander Dewdney,
    Mathematical Recreations,
    Scientific American,
    Volume 262, Number 5, May 1990, pages 126-129.
  6. Bernt Wahl, Peter VanRoy, Michael Larsen, Eric Kampman,
    Exploring Fractals on the Mac,
    Addison Wesley, 1995,
    ISBN: 0201626306,
    LC: QA614.86.W34.

Source Code:


Last revised on 23 August 2025.