Pythagoras tree (fractal)

A Pythagoras tree is a special type of fractal.

The original method for creating a Pythagoras tree is based on the Pythagorean Theorem, are arranged in a square on the two smaller squares at a right angle. By recursively invoking this procedure a fractal structure is generated which is similar to the limiting case of the form of a tree. With the right angle of the triangle enclosed the total area of ​​each level remains the same, therefore, the area of the base ( trunk) is exactly as large as the sum of the areas of all exterior elements (leaves).

Construction

From a baseline of a square is constructed. On this base element ( strain) a Thales circle is drawn and this arbitrarily divided on the top. The resulting point is connected to the base member ( Figure 1), so that a right-angled triangle. From the two legs of the triangle formed each a square is calculated (Figure 2), a Thales circle is again recorded, shared this, a right triangle is calculated (Figure 3 ), and so back to square one extended ( Fig. 4). This process is repeated as often as desired.

Other forms

Since such a tree, which was produced strictly according to Pythagoras, looks very unnatural, it could even be deviated from the original form.

  • Right-angled isosceles triangles
  • Different colors
  • Free angle
  • No squares
  • Right-angled triangles
  • Different colors
  • No right-angled triangles
  • Different colors
  • Random log lengths and random strain splitting ratios
  • Right-angled triangles
  • Different colors
  • Isosceles triangles
  • Right-angled triangles
  • Different colors
Recursion
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