# CTREE

## Purpose:

Creates a binary fractal.

## Syntax:

CTREE(stages, cangle,
cindex)

stages |
- |
Optional. An integer, the depth of fractal
recursion. Defaults to 6. |

cangle |
- |
Optional. A real, the angle increment per
radians. Defaults to 4. |

cindex |
- |
Optional. An integer, the starting color index.
Defaults to 15, white. |

## Returns:

Multiple overplotted XY series.

## Example:

ctree

displays a depth 6 binary C-Tree.

## Example:

ctree(9)

displays a depth 9 binary C-Tree.

## Remarks:

CTREE draws a binary fractal called the Pythagorean Tree created by
A. E. Bosman. The fractal is produced by starting with a square of width
W. Two smaller squares of width W * sqrt(2)/2 are connected to one side of
the first square to form a 45-45-90 triangle. The process is repeated
with each of the smaller squares over and over again. Because each new
stage creates twice as many squares as the preceding stage, the Pythagorean
Tree is considered a binary fractal.

The SPL code is based on an algorithm by Hans Lauwerier.

## See Also:

OVERPLOT

XY

## References:

Hans Lauwerier

Fractals: Endlessly Repeated Geometrical
Figures.

Princeton University Press, 1991

p111-112