A theoretical framework mapping Grammar based systems and Fractal description

Abstract : In this work, we propose a new method to describe fractal shapes using parametric L-systems. This method consists of introducing scaling factors in the production rules of the parametric L-system grammars. We present a turtle monoid on which we base our calculations to show the exact mathematical relation between L-systems and iterated function systems (IFS); we then establish the conditions for the scaling factors to produce plants' and curves' fractal shapes from parametric L-systems. We demonstrate that with specific values of the scaling factors, we find the exact relationship established by Prusinkiewicz and Hammel between L-systems and IFS. Finaly, we present some examples of fractal plant forms ans curves created using parametric L-systems with scaling factors.
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Ikbal Zammouri, Eric Tosan, Béchir Ayeb. A theoretical framework mapping Grammar based systems and Fractal description. Fractals, World Scientific Publishing, 2008, 4, 16, pp.389-401. ⟨10.1142/S0218348X08004058⟩. ⟨hal-01507174⟩



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