Fractals and L-systems

Abstract

In geometry objects are often defined by explicit rules and transformations which can easily be translated into mathematical formulas. For example, a circle is the set of all points which are at a fixed distance r from a centre (a, b).

$$ K = \{(x, y) \in \mathbb R^2 \;;\; (x - a)^2 + (y -b)^2 = r^2\} $$

or

$$ K = \{(x, y) \in \mathbb R^2 \;;\; x = a + r \cos \varphi ,\ y = b + r \sin \varphi , \ 0 \le \varphi < 2\pi \}. $$