Spatial Pattern Formation via Reaction–Diffusion Dynamics in 32<tex>$,times,$</tex>32<tex>$,times,$</tex>4 CNN Chip

2004 ◽  
Vol 51 (5) ◽  
pp. 939-947 ◽  
Author(s):  
B.E. Shi ◽  
T. Luo
Keyword(s):  
Pattern Formation ◽  
Spatial Pattern ◽  
Reaction Diffusion ◽  
Diffusion Dynamics ◽  
Spatial Pattern Formation

scholarly journals HIERARCHICAL MODELS FOR SPATIAL PATTERN FORMATION IN BIOLOGY

1995 ◽  
Vol 03 (04) ◽  
pp. 987-997 ◽  
Author(s):  
P. K. MAINI
Keyword(s):  
Pattern Formation ◽  
Spatial Heterogeneity ◽  
Spatial Pattern ◽  
Diffusion Model ◽  
Hierarchical Models ◽  
Reaction Diffusion ◽  
Skeletal Patterning ◽  
Reaction Diffusion Model ◽  
Spatial Pattern Formation ◽  
Set Up

We review some recent work investigating a hierarchy of patterning processes in which a reaction-diffusion model forms the top level. In one such hierarchy, it is assumed that the boundary is differentiated, and it is shown that this can greatly enhance the robustness of the patterns subsequently formed by the reaction-diffusion model. In the second, a spatial heterogeneity in background environment is first set-up by a simple gradient model. The resulting patterns produced by the reaction-diffusion system may be isolated to specific parts of the domain. The application of such hierarchical models to skeletal patterning in the tetrapod limb is considered.

Spatial-Pattern-Induced Evolution of a Self-Replicating Loop Network

2006 ◽  
Vol 12 (4) ◽  
pp. 461-485 ◽  
Author(s):  
Keisuke Suzuki ◽  
Takashi Ikegami
Keyword(s):  
Pattern Formation ◽  
Spatial Pattern ◽  
Spatial Patterns ◽  
Spiral Structure ◽  
Scale Interactions ◽  
Micro Scale ◽  
Macro Scale ◽  
Loop Network ◽  
Spatial Pattern Formation

We study a system of self-replicating loops in which interaction rules between individuals allow competition that leads to the formation of a hypercycle-like network. The main feature of the model is the multiple layers of interaction between loops, which lead to both global spatial patterns and local replication. The network of loops manifests itself as a spiral structure from which new kinds of self-replicating loops emerge at the boundaries between different species. In these regions, larger and more complex self-replicating loops live for longer periods of time, managing to self-replicate in spite of their slower replication. Of particular interest is how micro-scale interactions between replicators lead to macro-scale spatial pattern formation, and how these macro-scale patterns in turn perturb the micro-scale replication dynamics.

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