Bret Victor has an interesting contribution to the “Kill Math” project in the form of an iPad App that combines smooth user interface design with clever visuals for dynamic realtime visualization of systems of differential equations.
A user interface for exploring systems of differential equations. Every variable is shown as a plot; every parameter has a knob that can be adjusted in realtime. This ubiquitous visualization and in-context-manipulation helps the user develop a sense for how the parameters of the system influence its behavior.
Everyone that has taken advanced Calculus remembers those nightmarish problems of revolving curves around axes, and integrated the resulting volumes. An unlikely article in the New York Times discusses this with the signature project of the class, computing the volume of the space between two perpendicular intersecting cylinders, and gets into how you go about visualizing such a problem.
Archimedes managed to find it, but only by virtue of his astounding ingenuity. He used a mechanical method based on levers and centers of gravity, in effect weighing the shape in his mind by balancing it against others he already understood. The downside of his approach, besides the prohibitive brilliance it required, was that it applied only to a limited range of shapes.
As visualization scientists and visual effects artists, we spend much of our time trying to use math to recreate physical nature and effects, we don’t spend much time trying to derive math from nature. A new short film from Cristobal Vila and Eterea studios aims do to just that by showing us how the fibonnaci sequence, the golden ratio, and other famous geometric and mathematical constructs can be found in objects like shells, leaves, flowers, and insects. Some beautiful CG combined with gorgeous music and compositing effects brings this to the screen.
See it below, and then be sure to read his writeup about the various formula’s within the film.
Everyone knows the famous 2D Mandlebrot fractal, but it’s 3D equivalent has been difficult to find. Daniel White has been working on it for the last few years with help from several mathematicians and has finally stumbled onto a formula that looks like it could be the elusive 3D Mandlebrot, the Mandelbulb.
Our story starts with a guy named Rudy Rucker an American mathematician computer scientist and science fiction author and in fact one of the founders of the cyberpunk science-fiction movement . Around 20 years ago along with other approaches he first imagined the concept behind the potential 3D Mandelbulb barring a small mistake in the formula which nevertheless still can produce very interesting results – see later and also wrote a short story about the 3D Mandelbrot in 1987 entitled “As Above So Below” also see his blog entry and notebook . Back then of course the hardware was barely up to the task of rendering the 2D Mandelbrot let alone the 3D version – which would require billions of calculations to see the results making research in the area a painstaking process to say the least.
Hit his site for several more pictures and details.
Bret Victor has an interesting contribution to the “Kill Math” project in the form of an iPad App that combines smooth user interface design with clever visuals for dynamic realtime visualization of systems of differential equations.
As visualization scientists and visual effects artists, we spend much of our time trying to use math to recreate physical nature and effects, we don’t spend much time trying to derive math from nature. A new short film from Cristobal Vila and 
Everyone knows the famous 2D Mandlebrot fractal, but it’s 3D equivalent has been difficult to find. Daniel White has been working on it for the last few years with help from several mathematicians and has finally stumbled onto a formula that looks like it could be the elusive 3D Mandlebrot, the Mandelbulb.
VizWorld.com 
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