Fractals using programmable typesetting in Mathematica 3.0

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

1/(1 + 1/(1 + 1/(1 + 1/(...))))

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:

  GridBox[{{#,#,#},{#," ",#},{#,#,#}}]&,
  "\[FilledSquare]", 3],
    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.

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