
Simple recursive construction of a space filling triangle. There is
no user interaction.
For any given triangle ABC, pick a random midpoint D and divide into
three smaller triangles, so that triangles ADC, ABD, and DBC now exist.
Repeat the procedure for each of the new triangles.



figure a.
the triangular substitution model of Triangulation 


The resulting computational structure is nested in nature. Triangle
points closer to the beginning of the sequence are highlighted by
glowing rays. This is because they are shared by larger number of
child triangles.
The graphic representation of this process uses a single movieclip
for all three triangle divisions. When a triangle is divided, a Movieclip
is placed at the origin of the stage and instructured to draw segments
DA, DB, and DC. Drawing the triangle this way avoids the overlapping
borders caused by drawing the perimeter.
A maximum recursive depth of 8 calls is enforced to keep the structure
reasonable. 








jtarbell,
march 2003 

