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 [...]
I just finished reading “Shadow of the Wind” by Carlos Ruiz Zafón. I would highly recommend this book to anyone who is a fan of fiction. Exceptional style of writing wraps twists of story-line unraveling the mystery in rich poetic and metaphoric language. Besides dramatic roller-coaster of events and emotions, the book constantly induces thoughts and imagery and [...]
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]
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 [...]
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 [...]
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 [...]
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 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 [...]
I made another video with Mathematica. The six changing shapes in the video are called attractors. They are graphical forms of a simple mathematical formula attributed to Peter de Jong. At any given moment the way a single attractor looks depends only on four numbers. A slight variation in these numbers can remarkably change the [...]
“Mathematica Render” channel and group were recently created on Vimeo to gather a community of enthusiasts designing videos using Wolfram Research Mathematica software. The goal is to promote Mathematica examples of dynamic visualizations that can be used in research, education and art. With such Mathematica capabilities as simulated camera, lighting, image processing, various export options, [...]
![Trams in Savannah are Newyearly Christmasy. To provide streetcar service a 1930s-era W5-class streetcar (#756), originally from Melbourne, Australia, was purchased by the city for about $207,000 and converted to power its motors with an onboard biodiesel-fueled generator and batteries as a hybrid drive for an additional $100,000.[5] Hence it is a form of diesel railcar. The streetcar was nicknamed "Dottie" — a reference to the Savannah DOT that completed the project.](http://distilleryimage1.s3.amazonaws.com/a5192358537a11e28e2c22000a1fb747_5.jpg "Trams in Savannah are Newyearly Christmasy. To provide streetcar service a 1930s-era W5-class streetcar (#756), originally from Melbourne, Australia, was purchased by the city for about $207,000 and converted to power its motors with an onboard biodiesel-fueled generator and batteries as a hybrid drive for an additional $100,000.[5] Hence it is a form of diesel railcar. The streetcar was nicknamed \"Dottie\" — a reference to the Savannah DOT that completed the project.")
