Fractal Polygons

With turtle graphics it is quite easy to construct in a recursive manner regular polygones.

It is possible to play around with this example: In the last line of the input window there is the command

fracPolygone(5,100,0.4,5);

The meaning of the parameters is

• 5: number of vertices of the regular polygone,
• 100: length of a side of the initial polygone,
• 0.4: shrink factor from one level to the next,
• 5: number of recursion steps.

function fracPolygone(corner,len,shrink,recurs) { if (recurs>0) { if (arguments.length==4) { // initial call t.rt(180); fracPolygone(corner,len*shrink,shrink,recurs-1,1); t.lt(180); } t.fd(len); t.rt(360/corner); for(var i=0;i<corner-1;i++) { t.rt(180); fracPolygone(corner,len*shrink,shrink,recurs-1,1); t.lt(180); t.fd(len); t.rt(360/corner); } }; } t.cs(); t.hideTurtle(); t.setPos(-100,0); t.setPenColor('blue'); fracPolygone(5,100,0.4,5);

References

• Peter Baptist, Wolfgang Neidhardt, Alfred Wassermann: Symmetry and Regular Polygons, Prispevki k poucevanju Matematike, The Improvement of Mathematics Education in Secondary Schools: A Tempus Project, Maribor 1996.