Rock-paper-scissors reaction-diffusion equation on the sphere
Submitted by Nils Berglund on
Solution of a reaction-diffusion equation involving three chemicals, each of them dominating one of the others, and dominated by the other one.
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Allen-Cahn equation on the sphere
Submitted by Nils Berglund on
3D render of the Allen-Cahn equation on the 2-sphere. The color hue and radial coordinate indicate the value of the field, with red corresponding to positive values, and blue to negative values.
Waves with cubic symmetry on the sphere, 2d projection
Submitted by Nils Berglund on
Solution of the wave equation on a sphere. Reflecting obstacles have been placed around the vertices of a cube. The initial state is a set of circular waves of alternating sign, concentrated at the centers of the faces of the cube and on the centers of its edges. The video shows an equirectangular projection.
Waves with octahedral symmetry on the sphere, 2d projection
Submitted by Nils Berglund on
Solution of the wave equation on a sphere. Reflecting obstacles have been placed around the vertices of a regular octahedron. The initial state is a set of circular waves of alternating sign, concentrated at the centers of the faces of the octahedron. The video shows an equirectangular projection.
Waves with dodecahedral symmetry on the sphere, 2d projection
Submitted by Nils Berglund on
Solution of the wave equation on a sphere. Reflecting obstacles have been placed around the vertices of a regular dodecahedron. The initial state is a set of circular waves concentrated at the centers of the faces of the dodecahedron. The video shows an equirectangular projection.
Waves with icosahedral symmetry on the sphere, 2d projection
Submitted by Nils Berglund on
Solution of the wave equation on a sphere. Reflecting obstacles have been placed around the vertices of a regular icosahedron. The initial state is a set of circular waves concentrated at the centers of the faces of the icosahedron. The video shows an equirectangular projection.
Waves with cubic symmetry on a sphere
Submitted by Nils Berglund on
Solution of the wave equation on a sphere. Reflecting obstacles have been placed around the vertices of a cube. The initial state is composed circular waves concentrated at the centers of the faces of the cube, and on the midpoints of its edges. The colors and radial coordinate represent the wave height and averaged wave energy.
Waves in a Julia set on the Riemann sphere, 2d projection
Submitted by Nils Berglund on
A solution of the wave equation in a domain on the Riemann sphere, which is given by an approximation of a Julia set with parameter 0.37468 + 0.21115 i. The initial state is given by two circular waves, with opposite longitudes and positive latitude, and opposite sign. The video shows an equirectangular projection of the sphere.
Waves outside a disconnected Julia set on the Riemann sphere
Submitted by Nils Berglund on
A solution of the wave equation in a domain on the Riemann sphere, which is given by the complement of an approximation of a Julia set with parameter -0.77145 -0.10295 i. The initial state is given by two circular waves, with opposite longitudes and zero latitude, and opposite sign.
Waves with octahedral symmetry on the sphere
Submitted by Nils Berglund on
Solution of the wave equation on a sphere. Reflecting obstacles have been placed around the vertices of a regular octahedron. The initial state is a set of circular waves concentrated at the centers of the faces of the octahedron. The colors and radial coordinate represent the wave height and averaged wave energy.