Reaction-diffusion in a growing 3D domain of skin scales generates a discrete cellular automaton

We previously showed that the adult ocellated lizard skin colour pattern is effectively generated by a stochastic cellular automaton (CA) of skin scales. We additionally suggested that the canonical continuous 2D reaction-diffusion (RD) process of colour pattern development is transformed into this discrete CA by reduced diffusion coefficients at the borders of scales (justified by the corresponding thinning of the skin). Here, we use RD numerical simulations in 3D on realistic lizard skin geometries and demonstrate that skin thickness variation on its own is sufficient to cause scale-by-scale coloration and CA dynamics during RD patterning. In addition, we show that this phenomenon is robust to RD model variation. Finally, using dimensionality-reduction approaches on large networks of skin scales, we show that animal growth affects the scale-colour flipping dynamics by causing a substantial decrease of the relative length scale of the labyrinthine colour pattern of the lizard skin.

Car accident in synchronized traffic flow: A stochastic cellular automaton model

In this paper, we study the probability of car accidents in the modified Nagel–Schreckenberg (mNaSch) under the periodic boundary condition. In order to understand the quality of interaction between vehicles in each phase of the mNaSch, the velocity correlation coefficients were investigated. The effect of the evacuation of damaged vehicles was also studied. The fundamental diagram of the system is constructed in both cases with and without the evacuation. We found that the synchronized phases in the mNaSch are manifested into two aspects. In the first phase, the velocity correlation coefficients are zero where all vehicles move at the same speed. Hence, in the other phase, the speed of vehicles shows a synchronization as the form of clusters of moving vehicles where two speeds predominate simultaneously and the velocity correlation coefficients are higher. In addition, the car accidents in the modified mNaSch depend strongly on the initial configuration especially, if we consider those car accidents really happening in the system. The evacuation of damaged vehicles enhances the traffic situation and qualitatively changes the traffic phases in the mNaSch.

CellLab-CTS 2015: continuous-time stochastic cellular automaton modeling using Landlab

CellLab-CTS 2015 is a Python-language software library for creating two-dimensional, continuous-time stochastic (CTS) cellular automaton models. The model domain consists of a set of grid nodes, with each node assigned an integer state code that represents its condition or composition. Adjacent pairs of nodes may undergo transitions to different states, according to a user-defined average transition rate. A model is created by writing a Python code that defines the possible states, the transitions, and the rates of those transitions. The code instantiates, initializes, and runs one of four object classes that represent different types of CTS models. CellLab-CTS provides the option of using either square or hexagonal grid cells. The software provides the ability to treat particular grid-node states as moving particles, and to track their position over time. Grid nodes may also be assigned user-defined properties, which the user can update after each transition through the use of a callback function. As a component of the Landlab modeling framework, CellLab-CTS models take advantage of a suite of Landlab's tools and capabilities, such as support for standardized input and output.

CellLab-CTS 2015: a Python library for continuous-time stochastic cellular automaton modeling using Landlab

CellLab-CTS 2015 is a Python-language software library for creating two-dimensional, continuous-time stochastic (CTS) cellular automaton models. The model domain consists of a set of grid nodes, with each node assigned an integer state-code that represents its condition or composition. Adjacent pairs of nodes may undergo transitions to different states, according to a user-defined average transition rate. A model is created by writing a Python code that defines the possible states, the transitions, and the rates of those transitions. The code instantiates, initializes, and runs one of four object classes that represent different types of CTS model. CellLab-CTS provides the option of using either square or hexagonal grid cells. The software provides the ability to treat particular grid-node states as moving particles, and to track their position over time. Grid nodes may also be assigned user-defined properties, which the user can update after each transition through the use of a callback function. As a component of the Landlab modeling framework, CellLab-CTS models take advantage of a suite of Landlab's tools and capabilities, such as support for standardized input and output.