Bernoulli bond percolation on a square lattice
Submitted by Nils Berglund on
Bernoulli bond percolation on a square lattice, for different lattice sizes.
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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.
A circular lens, wave height and cumulative energy in 3D
Submitted by Nils Berglund on
This simulation shows the working of a lens made of a circular segment, that is, a disc cut by a straight line. The lens works here like the objective of a camera, by concentrating an incoming planar wave at the focal point of the lens. The index of refraction of the lens is equal to 5/3 = 1.666…, so that according the the lensmaker’s equation, the focal length should be equal to 1.5 times the radius of the circle.
Colorful Brownian Motion
With this web demo, you can play around with and learn something about Brownian Motion, a fundamental concept in the theory of stochastic processes and probabilistic physics.
Hybrid Pseudo Kleinian
Submitted by Torsten Stier on
a pragmatic approach of a 3d fractal hybrid, which combines the formal properties of two fractals in one system.