Ice Fractal

$\begin{figure}\begin{center}\BoxedEPSF{IceTriangle.epsf scaled 700}\end{center}\end{figure}$

$\begin{figure}\begin{center}\BoxedEPSF{IceAntiTriangle.epsf scaled 700}\end{center}\end{figure}$

$\begin{figure}\begin{center}\BoxedEPSF{IceSquare.epsf scaled 700}\end{center}\end{figure}$

$\begin{figure}\begin{center}\BoxedEPSF{IceAntiSquare.epsf scaled 700}\end{center}\end{figure}$

A Fractal (square, triangle, etc.) based on a simple generating motif. The above plots show the ice triangle, antitriangle, square, and antisquare. The base curves and motifs for the fractals illustrated above are shown below.

$\begin{figure}\begin{center}\BoxedEPSF{IceTriangleMotif.epsf scaled 490}\qquad\BoxedEPSF{IceAntiTriangleMotif.epsf scaled 490}\end{center}\end{figure}$

$\begin{figure}\begin{center}\BoxedEPSF{IceSquareMotif.epsf scaled 490}\qquad\BoxedEPSF{IceAntiSquareMotif.epsf scaled 490}\end{center}\end{figure}$

See also Fractal

References

Lauwerier, H. Fractals: Endlessly Repeated Geometric Figures. Princeton, NJ: Princeton University Press, p. 44, 1991.

Weisstein, E. W. ``Fractals.'' Mathematica notebook Fractal.m.