L-systems (or Lindenmayer systems) are conceived as a mathematical theory of plant development. The main concept is rewriting, a technique for defining complex objects by successively replacing parts of a simple initial object using a set of rewriting rules or productions. An example of this is the snowflake curve. This 'curve' begins with 2 shapes; an initiator and a generator. The generator is an oriented broken line made up of N equal sides of length r. The structure starts with a broken line and continues in replacing each straight interval with a copy of the generator, reduced and displaced so as to have the same end points as those of the internal being replaced. (see Fig 1.1)
Image reference: from website: http://algorithmicbotany.org/papers/abop/abop.pdf, The Algorithmic Beauty of Plants, Chapter 1: Graphical Modeling Using L-Systems, p 2.Fibonacci numbers is a series beginning with 0 and 1, then uses the simple rule: Add the last 2 numbers to get the next. This can be seen in the spiral that is created by the seeds in the centre of a sunflower. This can be shown by this linear recurrence equation:
Fn = Fn-1 + Fn-2
References:
http://plus.maths.org/content/os/issue3/fibonacci/index
http://mathworld.wolfram.com/FibonacciNumber.html
http://www.maths.surrey.ac.uk/hosted-sites/R.Knott/Fibonacci/
http://www.wolframscience.com/nksonline/page-2#previous
http://algorithmicbotany.org/papers/abop/abop.pdf
http://www.grasshopper3d.com/page/library-algorithms-and
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