Recursive turtle programs and iterated affine transformations Academic Article uri icon


  • 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. 2004 Elsevier Ltd. All rights reserved.

published proceedings

  • Computers & Graphics

altmetric score

  • 6

author list (cited authors)

  • Ju, T., Schaefer, S., & Goldman, R.

citation count

  • 7

complete list of authors

  • Ju, Tao||Schaefer, Scott||Goldman, Ron

publication date

  • December 2004