Graphical applications of L-systems
Proceedings on Graphics Interface '86/Vision Interface '86
Fractals everywhere
The object instancing paradigm for linear fractal modeling
Proceedings of the conference on Graphics interface '92
The algorithmic beauty of plants
The algorithmic beauty of plants
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We provide a formal proof of equivalence between the class of fractals created by recursive-turtle programs (RTP) and iterated affine transformations (IAT). We begin by reviewing RTP (a geometric interpretation of non-bracketed L-systems with a single production rule) and IAT (iterated function systems restricted to affine transformations). Next, we provide a simple extension to RTP that generalizes RTP from conformal transformations to arbitrary affine transformations. We then present constructive proofs of equivalence between the fractal geometry generated by RTP and IAT that yield conversion algorithms between these two methods. We conclude with possible extensions and a few open questions for future research.