Subject: bush fractals

My son has a report due on fractals. He needs information on bush fractals, but we cannot seem to find anything out about them.

my name is Anita Wisecup I am his Mother, my son is in 8th grade

I found a little bit about bush fractals, but not as much as I had hoped. The first two references are really just diagrams of some bush fractals

• http://library.thinkquest.org/26242/full/gallery/g7.html
  
  
• http://library.thinkquest.org/12740/netscape/gallery/lsystem.html

The third reference http://id.mind.net/~zona/mmts/geometrySection/fractals/tree/treeFractal.html contains a java applet which lets you manipulate some of the factors in the creation of such a fractal and see how changes to these factors change the fractal.

To construct their fractal bush they start with a V with an angle of 25^o between the branches, and branches of length 60 units. (I am not sure what the units are but that is not important. It can be any convenient length.) At the end of each branch place another V, with the same angle between the branches. The "shrink factor" tells you the length of the branches at this level. They have a shrink factor of 1.5 = ³/₂, which means that the branches at the first level are 1.5 times the length of the branches at the second level. In other words the branches at the second level are  ²/₃'s the length of the branches at the first level.

At the four ends of branches at the second level, place V's with the same angle separation and branch lengths  ²/₃'s the lengths of the branches at the second level. This process is repeated until any new branch would have length less than 3 units. (minimum size = 3.) To construct the entire fractal the process is repeated indefinitely.

These structures have the fundamental property of self-simularity. If you prune the bush at any level by cutting it at the base of a V, the piece cut off, if magnified the proper amount, is identical to the entire bush.