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The logic of living assembly
Published in Martyn Dade-Robertson, Living Construction, 2020
If the design of biological assembly depends on us identifying where information is located, then emergence provides a problem because, as I will show, in emergent systems, some information is not present in the system of assembly until the parts have assembled. We can create synthetic systems which exhibit emergent behaviours, including, for example, computer simulations such as Turing patterns (Turing, 1952), and these models are often used as a way of describing the formation of patterns in nature.
Reaction–Diffusion Modeling
Published in Ranjit Kumar Upadhyay, Satteluri R. K. Iyengar, Spatial Dynamics and Pattern Formation in Biological Populations, 2021
Ranjit Kumar Upadhyay, Satteluri R. K. Iyengar
with no-flux conditions at the boundary and positive initial conditions. Numerical simulations were used to study the formation of the Turing patterns. For the spatial model, they discussed the stability and Hopf bifurcation and determined the direction of the Hopf bifurcation curves.
Patterns in a freshwater tussock sedge model
Published in Applicable Analysis, 2022
Xiaojie Hou, Jinliang Wang, You Li
The mechanism of pattern formation has attracted considerable attention since the last decades. In the 1950s, A. M. Turing [16] discovered that some special patterns in chemical systems can be described by coupled reaction–diffusion equations. Turing showed that diffusion can destabilize an otherwise stable homogeneous stationary state of the reaction diffusion system and lead to the formation of spatial Turing patterns. This kind of instability is called Turing instability or diffusion driven instability. Reaction diffusion models are frequently used to study the spatial pattern formations in ecology [2,3,17], chemical reactions [12,13], predator–prey models [14,15,18,19], for more models in biology that support patterns, see [20]. The interaction of activator and inhibitor, originally conceived by Turing, provides a potential theoretical explanation for pattern formation [21].