Waves with icosahedral symmetry on the sphere, 2d projection

film

Waves with icosahedral symmetry on the sphere, 2d projection

Licence

Submitted by

Nils Berglund

This film is part of

Credits

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.

The simulation shows a solution of the wave equation on a sphere, obtained by a finite difference scheme. There are Dirichlet boundary conditions on a set of discs of constant radius placed on the vertices of a regular icosahedron. The initial state is a set of circular waves concentrated near the centers of the faces of the icosahedron, which form a regular dodecahedron.

The point of view rotates around the sphere in the course of the simulation. Part 1 shows the wave height, while part 2 shows the energy averaged from the beginning of the simulation.

Files

More Films

chasing daylight
Inside Neural Numbers
Asymmetric rock-paper-scissors-lizzard-Spock equation on the sphere
Transition from 3-branched to 5-branched spirals in the Rock-Paper-Scissors-Lizard-Spock equation on the sphere
The rock-paper-scissors-lizard-Spock reaction-diffusion equation on the sphere
Spirals in the rock-paper-scissors equation on the sphere
Vorticity of spirals in the rock-paper-scissors equation on the sphere
Rock-paper-scissors reaction-diffusion equation on the sphere
Allen-Cahn equation on the sphere
Waves with cubic symmetry on the sphere, 2d projection
Waves with octahedral symmetry on the sphere, 2d projection
Waves with dodecahedral symmetry on the sphere, 2d projection
Waves with icosahedral symmetry on the sphere, 2d projection
Waves with cubic symmetry on a sphere
Waves in a Julia set on the Riemann sphere, 2d projection
Waves outside a disconnected Julia set on the Riemann sphere
Waves with octahedral symmetry on the sphere
A meteor impact in the North Atlantic
Waves in a Julia set on the Riemann sphere
Energy flux of waves with dodecahedral symmetry on the sphere
Visualization of 4-dimensional regular tilings
Waves with icosahedral symmetry on the sphere
Waves with dodecahedral symmetry on the sphere
a kind of hope
Symmetry Animated
Rotating view of cluster growth in Bernoulli site percolation on a cubic lattice
Cluster size distribution in Bernoulli site percolation on a cubic lattice
Cluster growth for Bernoulli site percolation on a cubic lattice
Zooming out of percolation configurations on a lattice of triangles
Zooming out of percolation configurations on a honeycomb lattice
Cluster size distribution in Bernoulli site percolation on a Poisson disc process
Bernoulli site percolation on a Poisson disc process
Cluster size distribution in Bernoulli bond percolation on a square lattice
Cluster size distribution in Bernoulli site percolation on a lattice of triangles
Cluster size distribution in Bernoulli site percolation on a honeycomb lattice
Number of clusters for Bernoulli site percolation on a honeycomb lattice
Bernoulli bond percolation on a honeycomb lattice
Site percolation on a lattice of triangles
Bernoulli percolation on a honeycomb lattice
Bernoulli bond percolation on a square lattice
Percolation
Transition from 3-branched to 5-branched spirals in the Rock-Paper-Scissors-Lizard-Spock equation
Rock-Paper-Scissors-Lizard-Spock reaction-diffusion equation
The Allen-Cahn equation on the two-dimensional torus
A circular lens, wave height and cumulative energy in 3D
But what is a Neural Network?
MENACE: the pile of matchboxes which can learn
Ceramic tiles and geometry
Maps of the Earth
Release of the Documentary Film: "IMAGINARY Uruguay: A Mathematical Journey"
conform!
,
Maths Week at Work
secret alphabets
Earth Day 2019
JSBach333 - canone permutativo al triangolo from BACH333 - Canon Composition Competition 2018
Gerhard Widmer on Expressive Music Performance, the Boesendorfer CEUS, and a MIDI Theremin
,
Geometry and Imagination Exhibition Video – ICM2018
Journeys of Women in Mathematics
Bach Mass B Minor Canon
MathLapse: String vs Beads
,
,
,
,
Virtual Reality Exhibition of Imaginary
Knots in 4D
Fractal Fugues
The measurement of spaces
Do you have time?
Playing with the language of mathematics
Geometry of Architecture
EUHFORIA: modeling the dangers of the sun
The math of the shells
A Trip in Italy
Drone in Greenland
Promotional video on ordinary differential equations
The Penrose-Riemann Connection
Costa Surface Animation
Defining Manifold
Examples of manifolds
Dimension
PLATO on LSD - a MathLapse into the Ideal World
The Seven Geese Groups - MathLapse
Music of the Sphere - MathLapse
Connect the Dots
Symmetries in a snow crystal - MathLapse
Mandel Boxing -- MathLapse
MathLapse: The Helicoid
MathLapse - Inscribed Angle Theorem
MathLapse - Abyss of Infinity
MathLapse - Wind Generated Waves
The Art of the Wunderlich Cube - MathLapse
MathLapse - Propeller Mystery
Drawing with light and mirrors –– MathLapse
MathLapse - Monge's Theorem
Group Theory Live Performance –– MathLapse
Building a Kepler Poinsot Star –– MathLapse
Graph Theory MathLapse
Around the world in …N fractals for Mathlapse!
Universal Standing Wave Principle Mathlapse
MathLapse – Cybernetic Self-Similarity
MathLapse – Can Anybody See the Algebraic Curve’s Degree?
MathLapse – Cybernetic Ant Watching its own Creation
MathLapse_BINARY with Exploding Dots_GMP

Uncaught exception thrown in session handler.

PDOException: SQLSTATE[HY000]: General error: 1114 The table 'drim_sessions' is full: INSERT INTO {sessions} (sid, ssid, uid, cache, hostname, session, timestamp) VALUES (:db_insert_placeholder_0, :db_insert_placeholder_1, :db_insert_placeholder_2, :db_insert_placeholder_3, :db_insert_placeholder_4, :db_insert_placeholder_5, :db_insert_placeholder_6); Array ( [:db_insert_placeholder_0] => AcCeImx0yLbAOwNILperECknVQvdbADzwlUBvKL2Wig [:db_insert_placeholder_1] => AcCeImx0yLbAOwNILperECknVQvdbADzwlUBvKL2Wig [:db_insert_placeholder_2] => 0 [:db_insert_placeholder_3] => 0 [:db_insert_placeholder_4] => 216.73.216.142 [:db_insert_placeholder_5] => messages|a:1:{s:5:"error";a:2:{i:0;s:338:"<em class="placeholder">Notice</em>: file_put_contents(): write of 8192 bytes failed with errno=28 No space left on device in <em class="placeholder">boost_write_file()</em> (line <em class="placeholder">1363</em> of <em class="placeholder">/var/www/imaginary.org/deploy/releases/20221029131330/sites/all/modules/boost/boost.module</em>).";i:1;s:339:"<em class="placeholder">Warning</em>: file_put_contents(): Only -1 of 138274 bytes written, possibly out of free disk space in <em class="placeholder">boost_write_file()</em> (line <em class="placeholder">1363</em> of <em class="placeholder">/var/www/imaginary.org/deploy/releases/20221029131330/sites/all/modules/boost/boost.module</em>).";}} [:db_insert_placeholder_6] => 1774312156 ) in _drupal_session_write() (line 209 of /var/www/imaginary.org/deploy/releases/20221029131330/includes/session.inc).