There can be great variation in shape of leaves. Neverthless they are fairly simple shapes. How far are we in describing the shape of leaves in a mathematically rigorous way? Do we have a general formula that can be used to describe all shapes of leaves (or, at least, a reasonably large subset)?

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    $\begingroup$ ncbi.nlm.nih.gov/pmc/articles/PMC3419012 $\endgroup$ Apr 15, 2017 at 18:29
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    $\begingroup$ L-systems. Search on-line for examples, or read "The Algorithmic Beauty of Plants". There's a freely downloadable PDF version online somewhere. $\endgroup$
    – jamesqf
    Apr 15, 2017 at 19:53
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    $\begingroup$ I don't think there is one equation that describes all leaf patterns. As the article linked by @CountIblis says, the mathematical description of the final forms using fractals or "golden ratio" can be biologically misleading. More accurate mathematical models would consider the developmental dynamics. L Mahadevan from Harvard works on pattern development in different biological tissues (not just leaves). Have a look at his site. $\endgroup$
    Apr 17, 2017 at 5:27
  • $\begingroup$ Related: This post $\endgroup$
    – user25568
    May 12, 2017 at 19:38

1 Answer 1


There are algorithms which can be used to describe leaves, if that is what you mean.

The following description takes into account that leaf shape is not solely a function of genetics, but is also effected by environment. It also models how different growth rates within the cells have consequences. Mutant, cloning cells are also factored into the description.

The mathematical model has interesting allometric implications.

Here is a very readable paper (PDF),which endeavours to describe differences using mathematics and for which for which we can thank Cornell University Library for hosting the paper and Lawrence Livermore National Laboratory.


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