Re: [math-fun] Museum of Mathematics
Robert Munafo (mrob27@gmail.com) writes:
Here are two things I have been working on.
Both sound great! Here's something that I fantasize about in a similar vein: I picture a big touch-sensitive panel, five feet wide and stretching up to the ceiling. In one mode, it runs a big simulation of Life, and you can pause the action, toggle the states of specific bits with your fingers (perhaps referring to a nearby card that lists common fun configurations to insert into the Life universe), and then re-start the simulation to see what happens. In another mode, the panel runs a 1-D cellular automaton, drifting up the screen as it evolves. The way the panel disappears into the ceiling is integral to the "wow" effect I'd want to achieve. A big touch-sensitive wall might have other cool uses. For instance, I have a great app on my iPhone that lets me zoom in on the Mandelbrot set and various associated Julia sets, using the wonderful two-finger expand/contract gesture. (It almost makes me fancy that the iPhone was invented by someone who wanted to explore the Mandelbrot set in this very tactile way, and decided to invent a PDA that would let him do it!) It'd be good to have a user-controlled way to zoom in the Koch snowflake curve and the Weierstrass function and Bolzano's function (the first example of an everywhere-continuous, nowhere-differentiable function). Jim Propp
There are a bazillion things you can do with webcam and a projector. One I just thought of is taking bounding boxes around people laying on the floor as an affine transformation and then generating an IFS. Three people will give you some variant of the Serpinski triangle; four properly arranged will give you Barnsley's fern. One thing I'd like to try with a projector is to put multiple cameras in an arc in front of a rough surface covered in glitter illuminated by a digital projector. Then one can determine which projector pixels reflect into which camera pixels; it ought to give a cheap 3d display (though I can't vouch for the quality). Puzzle games like Block and Roll are a fun model of certain finite axiomatic systems, where the initial board layout encodes the set of axioms, each game position is a theorem, each move is a rule, and you're trying to prove a specific theorem. -- Mike Stay - metaweta@gmail.com http://www.cs.auckland.ac.nz/~mike http://reperiendi.wordpress.com
Funny, I thought of the affine transform too. I was going to have the visitor wave their hands in front of the camera to create bounding trapezoids (size determined by the size of whatever you're waving, and persistence determined by how long you kept waving near the same spot; they would disappear some time after being created). Then to create the actual image, each trapezoid contains the user's image, suitably faded and alpha-blended to maintain contrast with a uniform overall brightness. Mike, to make Barnsley's fern, two of the people would have to be very small (infants would do) and one would have to be even smaller and extremely thin (perhaps a pet garter snake trained to stay still :-) Or you could abandon the "lying on the ground" idea, and instead place the camera at waist level and allow people to change their size by walking towards and away -- but then the placement of the smaller bounding boxes is constrained roughly to a horizon line -- or else the museum has to contain a jungle gym or similar climbable 3-D lattice On Tue, Oct 19, 2010 at 12:00, Mike Stay <metaweta@gmail.com> wrote:
There are a bazillion things you can do with webcam and a projector. One I just thought of is taking bounding boxes around people laying on the floor as an affine transformation and then generating an IFS. Three people will give you some variant of the Serpinski triangle; four properly arranged will give you Barnsley's fern. [...]
-- Robert Munafo -- mrob.com Follow me at: mrob27.wordpress.com - twitter.com/mrob_27 - youtube.com/user/mrob143 - rilybot.blogspot.com
participants (3)
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James Propp -
Mike Stay -
Robert Munafo