This animation illustrates a deterministic geometric construction generated from the sequence of natural numbers. Each integer contributes one circular arc to a continuous trajectory. Prime...
Geometric visualization generated by the Prime Geometry algorithm using deterministic turning rules based on prime and composite numbers.
A collection of computational visualizations exploring deterministic geometric constructions generated from integer sequences. The images illustrate how simple local turning rules based on prime...
Solution of a reaction-diffusion equation involving five chemicals. Each chemical dominates one of the others, is dominated by another one, and does not interact with the other two.
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...
Solution of a reaction-diffusion equation involving five chemicals, each of them dominating two of the others, and dominated by the other two.
Solution of a reaction-diffusion equation involving three chemicals, each of them dominating one of the others, and dominated by the other one.
Solution of a reaction-diffusion equation involving three chemicals, each of them dominating one of the others, and dominated by the other one.
Solution of a reaction-diffusion equation involving three chemicals, each of them dominating one of the others, and dominated by the other one.
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...
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...
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,...
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...
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...
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...
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...
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...
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...
This is a simulation of the wave equation on a sphere, with reflecting boundary conditions given by the Earth’s continents. The initial state is a circular wave concentrated around a point...
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...
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...
This video shows the use of Tak4D to illustrate tilings in a 4 dimensional space. Three regular tilings are made, the first with hypercubes, the second with hexadecachorons and the third with...
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...
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...
Symmetry is an illustrated animation that showcases two of the four symmetries of the plane, reflection symmetry and rotation symmetry.
The connected component of one face for Bernoulli site percolation on a cubic lattice, for increasing parameter p and different lattice sizes.
Clusters and cluster size distribution in Bernoulli site percolation on a cubic lattice, for increasing parameter p and different lattice sizes.
The connected component of one face for Bernoulli site percolation on a cubic lattice, for increasing parameter p and different lattice sizes.
Backwards zooms for Bernoulli site percolation on a lattice of triangles
Backwards zooms for Bernoulli site percolation on a honeycomb lattice
Bernoulli site percolation on a Poisson disc process, for different lattice sizes. Open clusters are colored according to their size.
Bernoulli site percolation on a Poisson disc process, for different lattice sizes.
Bernoulli bond percolation on a square lattice, for different lattice sizes. Open clusters are colored according to their size.
Bernoulli site percolation on a lattice of equilateral triangles (whose centers form a hexagonal lattice), for different lattice sizes. Open clusters are colored according to their size.
Bernoulli site percolation on a honeycomb lattice, for different lattice sizes. Open clusters are colored according to their size.
Bernoulli bond percolation on a honeycomb lattice, for different lattice sizes. Open clusters are shown in different colors.
Bernoulli bond percolation on a honeycomb lattice, for different lattice sizes.
Bernoulli site percolation, on lattices of triangles of different sizes
Bernoulli percolation on a honeycomb lattice, for different lattice sizes
Bernoulli bond percolation on a square lattice, for different lattice sizes.
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...
Solution of a reaction-diffusion equation involving five chemicals, each of them dominating two others.
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,...
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...
Through the observation of tile patterns and the identification of the isometries involved in their composition, we intend to illustrate the natural connections between geometry and art and to...
Maths Week at work is a series of brief videos, aimed at showing to our teenagers the beauty and applicability of Mathematics, as well as the range of careers this discipline can open up.
This video was part of the exhibition “Geometry and Imagination: Patterns in Nature and Culture” presented during ICM 2018.
World Women in Mathematics : successes and barriers for women in mathematics from an international perspective, told in the words of the women themselves.
J. S. Bach probably is one of the composers with most affinity to mathematics. He developed the art of fugue in a programmatic way in his work “The Art of Fugue”. So he...
“Stringing” a 3-dimensional integer lattice of “beads” with a Hamiltonian path (one that crosses every vertex but only once) as a visual showcase of 1-1 correspondence with the integers.
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4D-knots: what are they? Can we visualize them?
Are there interesting math problems about them?
Fractal Fugues are self-similar structures made from a simple motif which generates copies of itself. These copies are transformed in the dimensions of time and pitch.
The territory, its limits and frontiers; the right for space - matematicaS project
Orientation regarding time used in different cultures and over history - matematicaS project
Through works by renowned architects such as Antoni Gaudí, Felix Candela and Oscar Niemeyer, this film intends to show the natural way in which the formulas, the geometry of forms and their...
This film illustrates how the great majority of seashells existing in nature can be generated by a fixed set of equations by simply varying some parameters. This gives one more example of how the...
”A trip in Italy” is a short video created by the students for the other students, for the purpose to arouse on environmental issues like: global warming,renewable energy,clean cities,public...
This module intends to promote the subject matter on ordinary differential equations at the beginning of the study of a corresponding chapter in a Calculus course.
The film is about discretization of patterns, colours and shapes. The animation illustrates that a 2D periodic pattern can be mapped seemless to a torus. Riemann surfaces are more suitable to...
The Costa Surface is a minimal surface discovered by brazilian researcher Celso Costa in 1982 and visualized by Hoffman and Meeks in the same decade.
This video in a loop shows how to construct manifolds by gluing the borders of polygons or polyhedrons.
The film is in a loop and depicts the concept of Dimension. Three objects are presented: the cube, the simplex and the cube. These are shown in dimensions 0, 1, 2, 3.
About 2400 years ago in Greece,
Plato perceived his vision of the Ideal World
in ELEUSIS under the influence of halucinogenic
substances such as ergot...
A MathLapse by Ulrike Bath and Kevin Guo about the Helicoid - a minimal surface. Minimal surfaces are soap film surfaces spanned in wire frames. The presented helicoid is amongst the oldest of...
MathLapse Festival 2016 Winner. Experiencing the Inscribed Angle Theorem.
The wind forces the water into circular motion, yet it generates waves.
We define a Wunderlich cube to be a cube whose surfaces contain raised impressions of the reflections of seed shapes resembling the letter S. The video shows how this cube can be rolled leaving a...
Just 30 pipe cleaners can be assembled to form a Kepler Point star
This is a short introduction into the wonderful world of graph theory. Hopefully this video will help you learn, or serve as a refresher for, some basics concepts in graph theory. Enjoy!
Mathlapse Competition 2016. Imaginary Conference Berlin 22/07/2016.
The video was selected for screening at the award ceremony.
In it we wander around the world using fractal geometry...
Standing wave theory and Morphodynamic archetypes Sphere-vortex connection
The tripartite communion between the sphere, spiral and language involves a conceptual leap clarifying the...
The video shows a polygonal line consisting of 24 segments constructed by turtle geometry (Refs.: “Turtle Geometry” by Harold Abelson and Andrea diSessa, The MIT Press,...
The video shows the construction of an algebraic curve by a mechanical linkage.
The video shows the construction of an algebraic curve by a mechanical linkage.
In this wordless animation we demonstrate the mathematics of binary place-value, and leave the viewer with a puzzle.
In 2d we can spin a ray about a point. If the ray contains a 1d profile, spinning gives a 2d object.
In 3d we can spin a half plane about a line. If we the half plane contains a 2d profile,...
Thus, the universe is reduced to expressing order through sphere, genuine brick of the open, immeasurable, infinite, construct, which inhabits the geometry of spheres with morphodynamic, disk or...
MathLapse Festival 2016 Winner. Parallel planes, which touch a surface of constant width from opposite sides, have always the same distance - a generalized diameter. The movie starts with curves...
There are two purposes in this animation
1. Use complex logarithm to see the relation between stereographic projection and Mercator map
2. By rotating small region to the poles we can...
Watch how the numbers 0, 1, 2, …, 21 leave behind residues (mod 22) when raised to the powers of 0, 1, 2, …, 21.
MathLapse Festival 2016 Winner. A Wild Knot is a circular curve in the three-dimensional space which is infinitely knotted. In this video we show a recipe to build some kind of Wild Knots, using...
