Editing Morphogenesis (section)

== Computer models ==

An approach to model morphogenesis in [[computer science]] or [[mathematics]] can be traced to [[Alan Turing]]'s 1952 paper, "The chemical basis of morphogenesis",<ref>{{cite journal |last=Turing |first=Alan Mathison |year=1952 |title=The chemical basis of morphogenesis |journal= [[Philosophical Transactions of the Royal Society B]]|volume=237 |issue=641 |pages=37–72 |doi=10.1098/rstb.1952.0012|bibcode=1952RSPTB.237...37T |s2cid=937133 }}</ref> a model now known as the [[Turing pattern]].

Another famous model is the so-called [[French flag model]], developed in the sixties.<ref>{{Cite journal | last1=Sharpe | first1=James | last2=Green | first2=Jeremy | title=Positional information and reaction-diffusion: two big ideas in developmental biology combine | journal=Development | volume=142 | pages=1203–1211 | doi=10.1242/dev.114991 | url=https://dev.biologists.org/content/142/7/1203 | date=2015 | issue=7 | pmid=25804733 | doi-access=free | hdl=10230/25028 | hdl-access=free }}</ref>

Improvements in [[computer performance]] in the twenty-first century enabled the simulation of relatively complex morphogenesis models.  In 2020, such a model was proposed where cell growth and differentiation is that of a [[cellular automaton]] with parametrized rules.  As the rules' parameters are differentiable, they can be trained with [[gradient descent]], a technique which has been highly optimized in recent years due to its use in [[machine learning]].<ref>{{cite journal | doi=10.23915/distill.00023 | title=Growing Neural Cellular Automata | year=2020 | last1=Mordvintsev | first1=Alexander | last2=Randazzo | first2=Ettore | last3=Niklasson | first3=Eyvind | last4=Levin | first4=Michael | journal=Distill | volume=5 | issue=2 | s2cid=213719058 | doi-access=free }}</ref>  This model was limited to the generation of pictures, and is thus bi-dimensional.

A similar model to the one described above was subsequently extended to generate three-dimensional structures, and was demonstrated in the video game ''[[Minecraft]]'', whose block-based nature made it particularly expedient for the simulation of 3D cellular automatons.<ref>{{cite arXiv | eprint=2103.08737 | last1=Sudhakaran | first1=Shyam | last2=Grbic | first2=Djordje | last3=Li | first3=Siyan | last4=Katona | first4=Adam | last5=Najarro | first5=Elias | last6=Glanois | first6=Claire | last7=Risi | first7=Sebastian | title=Growing 3D Artefacts and Functional Machines with Neural Cellular Automata | year=2021 | class=cs.LG }}</ref>