Bernoulli bond percolation on a honeycomb lattice
Submitted by Nils Berglund on
Bernoulli bond percolation on a honeycomb lattice, for different lattice sizes.
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Site percolation on a lattice of triangles
Submitted by Nils Berglund on
Bernoulli site percolation, on lattices of triangles of different sizes
Bernoulli percolation on a honeycomb lattice
Submitted by Nils Berglund on
Bernoulli percolation on a honeycomb lattice, for different lattice sizes
Bernoulli bond percolation on a square lattice
Submitted by Nils Berglund on
Bernoulli bond percolation on a square lattice, for different lattice sizes.
Percolation
Submitted by Nils Berglund on
Bernoulli site percolation on a square lattice, for different lattice sizes.
Transition from 3-branched to 5-branched spirals in the Rock-Paper-Scissors-Lizard-Spock equation
Submitted by Nils Berglund on
Solution of a reaction-diffusion equation involving five chemicals, each of them dominating two others. There are two interaction parameters, which are equal at the beginning of the simulation. As one of them decreases to zero, spirals with 5 branches appear.
Rock-Paper-Scissors-Lizard-Spock reaction-diffusion equation
Submitted by Nils Berglund on
Solution of a reaction-diffusion equation involving five chemicals, each of them dominating two others.
Polyhedral Realizations of Flat Tori
Submitted by Florent Tallerie on
Polyhedral Realizations of Flat Tori
Reaction-diffusion equations
Submitted by Nils Berglund on
This gallery contains visualizations of solutions of reaction-diffusion equations. These are partial differential equations for a field over a region in space, involving a diffusion term, given by a Laplace operator, which tends to make the field more homogeneous, and a reaction term, which models a physical, chemical or biological process that typically makes the field inhomogenous.
The Allen-Cahn equation on the two-dimensional torus
Submitted by Nils Berglund on
This is a 3D rendering of a solution of the Allen-Cahn equation in a rectangular domain with periodic boundary conditions. Both the z-coordinate and the color hue show the value of the solution, with blue indicating positive values, and red indicating negative ones. By increasing the viscosity (which measures the magnitude of diffusion) over time, one accelerates the coarse-graining dynamics of the system, separating blue and red phases. The luminosity depends on the angle between a normal vector to the surface and a fixed direction, to emulate the effect of a far away light source.