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African Fractals
Applications 4: Da Vinci branching

Sketch from Da Vinci's notebook showing his analysis of branching.

In botany the growing tip is called an "apical meristem." In "Edit Mode" you can see two red lines representing the apical meristems. Click off "snap to grid" and then change the size and angle of the red lines by dragging their endpoints.

In 1510 Leonardo Da Vinci wrote: "All the branches of a tree at every stage of its height when put together are equal in thickness to the trunk." Thus if a "mother" branch produces two "daughter" branches, the area of a cross-section of the mother is equal to the sum of the areas of the cross-sections of the daughters. This means that the ratio of the daughter diameter to the mother diameter will be about 0.707 -- can you show why? Can you find the ratio for mother branch length to daughter branch length? Try editing the seed shape to experiment with different branch diameter, length, and angle. Try different seeds from the "Seed" dropdown menu for higher branch numbers.