Posts Categorized: Mathematica

Who Owns the West? Federal Lands 2014

Posted by & filed under Code, Computation, Data, GIS, Mathematica, Wolfram, Wolfram Language.

This map is a spectacular example of how data reshape public perception and knowledge. Very simple in nature it nevertheless shocks an average citizen by giving clarity to the data usually buried in obscure tables. East versus west, federal versus private, – the contrast is sharp and reverberates in the minds entangled with American history. […]

Interactive 3D Calabi-Yau Surface

Posted by & filed under 3D, Code, Demonstrations Project, Graphics, Mathematica, Sketchfab, Wolfram, Wolfram Language.

Wolfram Language allows creation of computational 3D models. These are different from those you can build with your own hands such as SketchUp etc, because computations are often intrinsically different from the way humans see and think. Let’s take for example Calabi-Yau Surface. It is a mathematical object and it is hard to imagine it. […]

ASCII Tree

Happy ASCII New Year ;-)

Posted by & filed under Art, CDF, Code, Graphics, Mathematica, Wolfram, Wolfram Language.

I can occasionally appreciate a nice ASCII art design. But the better is the design, the more manual and custom approach it needs – or so it seems. It is actually quite challenging, if you think about it, to transform a known image or shape to a limited medium using finite set of geometries. So […]

Sin Tree

t * sin (t) = Christmas tree

Posted by & filed under Art, Code, Community, Graphics, Mathematica, Wolfram, Wolfram Language.

Another code sample from Wolfram Community. I noticed that a discussion about programming a lighted Christmas Tree from a simple equation t*Snt[t] became very popular on Reddit. It is connected to a project a programmer developed. I thought how fast we can make it with Wolfram language? Here is the result with slight flickering 😉 […]

Iconography for Elementary Cellular Automata Based on Radial Convergence Diagrams

Iconography for Elementary Cellular Automata Based on Radial Convergence Diagrams

Posted by & filed under App, CDF, Code, Demonstrations Project, Mathematica, Publishing, Wolfram.

My recent publication at the Wolfram Demonstrations Project: “Iconography for Elementary Cellular Automata Based on Radial Convergence Diagrams“.   Consider a complete set of initial conditions for a finite elementary cellular automaton (ECA). This set can be indexed by integers using a Gray code or a binary to decimal conversion. During the ECA evolution, the […]

Order, Chaos, and the Formation of a Cantor Set Attractor in Elementary Cellular Automata

Order, Chaos, and the Formation of a Cantor Set Attractor in Elementary Cellular Automata

Posted by & filed under App, CDF, Demonstrations Project, Mathematica, Publishing, Wolfram.

My recent publication at the Wolfram Demonstrations Project: Order, Chaos, and the Formation of a Cantor Set Attractor in Elementary Cellular Automata Consider finite elementary cellular automata (ECA) of size 10. All possible binary vectors of length 10 form a complete set of initial conditions (CSIC). Every step of an ECA evolution maps this set to […]

Time Series and Cobwebs for Arbitrary Recursive Maps on the Unit Interval

Posted by & filed under App, Demonstrations Project, Mathematica, Publishing, Wolfram.

My new publication at the Wolfram Demonstration Project is Time Series and Cobwebs for Arbitrary Recursive Maps on the Unit Interval. Follow the link to view interactive version. Here is an exert from text: “The logistic map is probably the most famous and simplest example of a function from the unit interval onto itself that […]

Complex numbers, beautiful surfaces and Mathematica

Posted by & filed under Code, Graphics, Mathematica, Wolfram.

A few lines of code in Mathematica can produce beautiful images. Take as an example this simple but spectacular result of singularities in complex plane: Plot3D[Im[Sec[(x + I y)^4]], {x, -2, 2}, {y, -2, 2}, Mesh -> None, ClippingStyle -> None, PlotStyle -> Directive[Orange, Opacity[.8], Specularity[White, 20]], PlotPoints -> 50]

visibility graph ECA

Horizontal Visibility Graphs for Elementary Cellular Automata

Posted by & filed under App, CDF, Demonstrations Project, Mathematica, Publishing, Widget, Wolfram.

My new publication at the Wolfram Demonstration Project is Horizontal Visibility Graphs for Elementary Cellular Automata. Follow the link to view interactive version. Here is an exert from text: “A time series can be formed from an evolution of a finite elementary cellular automaton (ECA). This can be done in a few different ways. We can […]

Automating xkcd Diagrams: Transforming Serious to Funny

Posted by & filed under Art, CDF, Mathematica, Press, Publishing, Wolfram.

An article I wrote for Wolfram Blog was just released. Here is the beginning: “On early Monday morning I noticed an interesting question posted on Mathematica Stack Exchange titled quite innocently “xkcd-style graphs.” Due to the popularity of Randall Munroe’sxkcd web comic, I expected a bit more than average of about ten or so up-votes, a few bookmarks. Little did I […]

Polyhedra obtained by stellation

Posted by & filed under 3D, App, CDF, Mathematica, Wolfram.

Stellation is the process of constructing polyhedra by extending the facial planes past the polyhedron edges of a given polyhedron until they intersect. The set of all possible polyhedron edges of the stellations can be obtained by finding all intersections on the facial planes. Since the number and variety of intersections can become unmanageable for […]

Lissajous Patterns on a Sphere Surface

Posted by & filed under 3D, App, Art, CDF, Demonstrations Project, Mathematica, Uncategorized, Wolfram.

Another Demonstration of mine was published at the Wolfram Demonstration Project. It helps to explore and create spherical artistic designs. I  generalized Lissajous curves to spherical coordinates. Azimuthal and polar angles undergo oscillations while the radius is kept constant. Although with the parameterization given I sought to emphasize the artistic side of Lissajous patterns, other spherical parameterizations […]

Stereoscopic 3D Macromolecule 1TF6

Posted by & filed under 3D, Mathematica, red-cyan, Stereoscopic, Video, Vimeo, Wolfram.

Stereoscopic 3D Macromolecule 1TF6 from Vitaliy Kaurov on Vimeo. To watch this video you need “red-cyan anaglyph glasses”.  This video was made with Mathematica 7. This type of red-cyan anaglyph videos can be useful for display of complex 3D structures. Once the structure is built it takes just a few lines of Mathematica code to […]