Embedded Files
Superlattice Turing patterns
Superlattice Turing patterns
Spatial resonances and superposition patterns in a reaction-diffusion model with interacting Turing modes
Spatial resonances and superposition patterns in a reaction-diffusion model with interacting Turing modes
On the chemical basis for morphogenesis, Turing structures, in some sense, shed light on How does the leopard get its spots? We focus on interacting Turing modes.
On the chemical basis for morphogenesis, Turing structures, in some sense, shed light on How does the leopard get its spots? We focus on interacting Turing modes.
The chlorite-iodide-malonic acid (CIMA) reaction exhibits an interesting Turing pattern, black-eye, where the black center (high concentration of iodide) is surrounded by a white ring(low concentration of iodide), and these eye-like spots arranged into a hexagonal lattice. [G. H. Gunaratne, Q. Ouyang, and H. L. Swinney, Phys. Rev. E 50, 2802 (1994)].
The chlorite-iodide-malonic acid (CIMA) reaction exhibits an interesting Turing pattern, black-eye, where the black center (high concentration of iodide) is surrounded by a white ring(low concentration of iodide), and these eye-like spots arranged into a hexagonal lattice. [G. H. Gunaratne, Q. Ouyang, and H. L. Swinney, Phys. Rev. E 50, 2802 (1994)].
A subsequent study[M. G. Gomes, Phys. Rev. E 60, 3741 (1999)] suggested that black-eye patterns are not two-dimensional,but rather projections of a three-dimensional body-centered cubic lattice. Recent experimental results suggest that the three-dimensional interpretation is not appropriate[C. Zhou, H. Guo, and Q. Ouyang, Phys. Rev. E 65, 036118 (2002)], but to date no model has been developed that reproduces the black-eye patterns in two dimensions.
A subsequent study[M. G. Gomes, Phys. Rev. E 60, 3741 (1999)] suggested that black-eye patterns are not two-dimensional,but rather projections of a three-dimensional body-centered cubic lattice. Recent experimental results suggest that the three-dimensional interpretation is not appropriate[C. Zhou, H. Guo, and Q. Ouyang, Phys. Rev. E 65, 036118 (2002)], but to date no model has been developed that reproduces the black-eye patterns in two dimensions.
We propose a model that generates not only black-eye patterns but also a variety of other spatial resonant patterns: “black eye”, “white-eye”, and “Twinkling-eye” resulting from interactions between different Turing modes, or between a single mode and its harmonics. Also, we obtained superposition patterns with different combination of stripe- and spot- Turing patterns.
We propose a model that generates not only black-eye patterns but also a variety of other spatial resonant patterns: “black eye”, “white-eye”, and “Twinkling-eye” resulting from interactions between different Turing modes, or between a single mode and its harmonics. Also, we obtained superposition patterns with different combination of stripe- and spot- Turing patterns.
This work appears in Phys. Rev. Lett. 88, 208303 ( 2002). (FILE NOT FOUND) Our results provide a possible mechanism not only for the recent experimental observation of ¡¡lack eye?patterns, but may also provide insights into the chemical basis of morphogenesis.
This work appears in Phys. Rev. Lett. 88, 208303 ( 2002). (FILE NOT FOUND) Our results provide a possible mechanism not only for the recent experimental observation of ¡¡lack eye?patterns, but may also provide insights into the chemical basis of morphogenesis.
Stationary internal spatial resonance patterns: black eyes, and white eyes
Stationary internal spatial resonance patterns: black eyes, and white eyes
Twinkling eyes (sub-harmonic resonance)
Twinkling eyes (sub-harmonic resonance)
Supperposition patterns
Supperposition patterns
The original Brusselator model
Page updated
Report abuse