Fractals using programmable typesetting in Mathematica 3.0

Back to Robert's Math Figures

A simple example of self-similarity in a typeset expression is a continued fraction, where each "denominator" resembles the whole expression:

Using the programmable typesetting system in Mathematica 3.0, you can create expressions that look like classic fractals. For instance, the Sierpinski gasket:

Nest[SubsuperscriptBox[#,#,#]&, "\[CapitalOmega]", 5] //DisplayForm

Sierpinski carpet:

StyleBox[
 Nest[
  GridBox[{{#,#,#},{#," ",#},{#,#,#}}]&,
  "\[FilledSquare]", 3],
  GridBoxOptions->{
    RowMinHeight->0, RowSpacings->0, ColumnSpacings->0}] //DisplayForm

With a little adjustment, you can get silly effects like the following:

Another doozy:

Designed and rendered using Mathematica 3.0 for the Apple Macintosh.

[Privacy Policy] [Terms of Use]

Home || The Math Library || Quick Reference || Search || Help 

© 1994-2008 Drexel University. All rights reserved.
http://mathforum.org/
The Math Forum is a research and educational enterprise of the Drexel School of Education.