Tuesday , May 11 2021

L-systems, Hacker News


        

Notes published

December****************************************************************************************************************************************************************************************************, 2019

Biologist

Aristid Lindenmayer

createdLindenmayer systems, orL-systems, in as a way of formalizing patterns of bacteria growth. L-systems are a recursive, string-rewriting framework, commonly used today in computer graphics to visualize and simulate organic growth, with applications inplant development,procedural content generation, andfractal-like art.************ (A rendering of several L-systems.)

The following describes L -system fundamentals, how they can be visually represented, and several classes of L-systems, like

context-sensitive L-systems

andstochastic L-systems. Much of the following has been derived fromPrzemyslaw Prusinkiewicz and Lindenmayer’s seminal work,The Algorithmic Beauty of Plants************************ String Rewriting [ F] ********************************

Fundamentally, an L-system is a set of rules that describe how to iteratively transforms a string of symbols. A string, in this context, is a series of symbols, like “**************************** (**************************************a(**************************************** (a) ***************************************************************************************************************a

(“or”) **************************** (************************************ (a) b (************************************** (a) *************************************** (b)a(a) ***************************************** (b) *************************************** (a) *****************************************aa (**************************************** (a) *************************************** (**************************************** (ababaabaaaa) ****************************************************************** ********************************************(a) ********** aba baa

a, and can be thought of as a word comprised of characters. Each rule, known as a (production) , describes the transformation of one symbol to another symbol, series of symbols, or no symbol at all. On each iteration, the productions are applied to each character simultaneously, resulting in a new series of symbols.

Productions in this rewriting system can be described with “before” and “after” states, often described as the predecessor and ************************************************ (successor) *************************************************; for example, the productiona) ***************************************** (⟶) *************************************************** (a) ***************************************** (b) ***************************************(a longrightarrow ab) ****************************************** (********************************************************************

************abrepresents that the symbol

********** (n. Given a word****************

a (******************************************** (a) *************************************************************************************************************)a

and productions****************

a (**************************************************

******************************************** (a)b () **************************************** a longrightarrow ab (********************************************************************************a⟶********

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