Joe wrote:

...
http://www.joelertola.com/temp/fractal_question.jpg

  But I noticed that there is a special number that will make the 
fractal fit perfectly in a triangle. I can use trial and error to get 
very close to this number but I would like to calculate it accurately 
if possible. The diagram shows the problem. In the program I move 
points B and C along line AD to draw different versions of the 
fractal shape. The number I want to calculate is the y value at point 
F. Does anyone have an idea on how to find that value?
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I fear your problem is underdetermined.

Is there any known angle (besides those of 90 deg)?

Best
-- 

                   Herbie

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          <http://www.gluender.de>