page_title: Barnsley fern
section_title: Mutant varieties
hierarchical_section_title: Barnsley fern / Construction / Mutant varieties
caption_attribution_description: English: Barnsley's fern illustrates the use of affine translations in an iterated function system (IFS) to create a fractal. This version has been created with the Barnsley transformation formula, but with a different coefficient matrix, resulting in longer leaflets, or pinnas. The parameters for this image are: 0 0 0 .25 0 -.4 .02 .95 .005 -.005 .93 -.002 .5 .84 .035 -.2 .16 .04 -.09 .02 .07 -.04 .2 .16 .04 .083 .12 .07
context_page_description: The Barnsley fern is a fractal named after the British mathematician Michael Barnsley who first described it in his book Fractals Everywhere. He made it to resemble the black spleenwort, Asplenium adiantum-nigrum.
context_section_description: By playing with the coefficients, it is possible to create mutant fern varieties. In his paper on V-variable fractals, Barnsley calls this trait a superfractal.
  One experimenter has come up with a table of coefficients to produce another remarkably naturally looking fern however, resembling the Cyclosorus or Thelypteridaceae fern. These are:
caption: Barnsley fern mutated into a Thelypteridaceae fern.
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