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4DVisualizationsAdanaxis 4D Space shooter Buddhabrot in 4D (in 3D, in 2D) The Mandelbrot fractal never looked so good. Definitely enjoyable stuff. Of course, you could just play Portal. Oh, sorry, that's just an ordinary 3D space which happens to be multiply disconnected and topologically unsettling. For more (Euclidian!) 4D visualization tools, (http://www.geom.uiuc.edu/docs/outreach/4-cube/squared.txt.html) [uiuc.edu] are a couple nice (but old) clips of rotating cubes and tesseracts through higher dimensions. For example, it gives you the (x,y,z) view of a cube then a simultaneous projection of that object in the (w,x) plane where w is a 4th orthogonal direction. It then proceeds to rotate the (w,x) projection in a circle to see what the 3D "shadow" in (x,y,z) space is doing. Rather than getting bigger and smaller (simulating perspective) as it moves back and forth in the 4th direction, the faces are color coded (I personally think this makes it easier to visualize). Run the simulation back and forth slowly a couple times and your brain locks in pretty well. For the same reasons you can't visualize a 3D object on a 1D space you can't visualize a 4D object on a 2D space. You cannot go up 2 dimensions. Just as we can visualize a 3D object on a 2D space we can visualize a 4D object on a 3D space. Thus we need something like this: http://dogfeathers.com/java/hyprcube.html
Anybody interested in visualizing hyperspace should learn about Alicia Boole Stott [agnesscott.edu] and her amazing story [ub.rug.nl]. She was the daughter of George Boole (of boolean algebra fame) who developed a mind-boggling series of paper cutout models of four dimensional objects that won her an honorary math doctorate in 1914. Check out these extensive photos of her work [math.rug.nl]. http://www.agnesscott.edu/lriddle/women/stott.htm |