Timm Dapper
www.td-grafik.de
Practical Procedural Modeling of Plants
22.01.2003 - Universität Bremen

Why is phi the best number?

  • best would be an irrational number that doesn't come
    close to a rational approximation (which would show up
    as arms) for as long as possible

  • "continued fractions" have this property

  • Example: p = 1 / (1 + 1 / (1 + 1 / (...))) so that p is just
    1 / (1 + p) so p² + p = 1

  • ...which is just another a definition of phi = (sqrt5 - 1) / 2