Thomas Müller Apps

Simulate a mathematical double pendulum onyour Android device. Change all the simulation parameters in thepreference settings. Use the gravity sensor for realisticsimulation depending on how you hold your device in your hand.Switch between Cartesian and polar grid background for betterorientation. Take a snapshot of your most curious pendulumsimulation.

VecFieldLIC visualizes 2D autonomousdynamicalsystems by means of the Line Integral Convolution (LIC)techniqueintroduced by Cabral and Leedom in 1993.A 2D autonomous dynamical system is defined by twocoupledfirst-order differential equations dx/dt = P(x,y) and dy/dt=Q(x,y) with P and Q being two arbitraryC^1-differentiablefunctions of x and y.These two functions can consist of all mathematicalfunctionsavailable from the OpenGL ES Shading Language.Note that you have to insert numbers as floats, e.g. "2" shouldread"2.0".

Simulate Brownian motion with particlesthatinteract only by elastic collision. Change thesimulationparameters in the preference settings. Use the gravitysensor foran additional force. Select between 5 differentpredefinedparameter settings where the yellow particle has X timesthe massof the other particles.

A black hole is the most weird object in the universe. An objectthat passes behind it appears strongly distorted because of theblack hole's influence on light propagation. Turn your smart phoneor tablet into a general relativistic simulator and move the blackhole around. The visualization is based on Einstein's generaltheory of relativity for a Schwarzschild black hole. The object isrepresented by an image that is put on a canvas behind the blackhole. The distance between the canvas and the black hole, as wellas the distance between the black hole and the observer, can bemodified. Of course, the black hole mass can also be changed. Forthe screenshots, NASA's "Blue Marble" photograph of Apollo 17 andthe Milky Way panorama by ESO/S.Brunier were taken. Your smartphone or tablet has to support 32 bit floating point operations onthe graphics card, otherwise, there will be artifacts or nothingwill be shown. Please note that you can use only images that fitinto the GPU texture memory of your device.

Simulate a thin accretion disk around a black hole on your Androiddevice. The visualizations are based on Einstein's general theoryof relativity for a Schwarzschild black hole. The apparentdistortion of the disk is due to light rays that follow the curvedspacetime. Because of the heavy use of the GPU the visualizationmight be slow or even show nothing on older devices. That might bedue to the insufficient precision of the graphics chip. In contrastto the 'Gargantua' black hole from the movie 'Interstellar', theblack hole has no proper spin, but it takes the lensing effect andthe Doppler shift into account which let the left part of the diskappear much brighter than the rest.

Have you ever wondered about how theworldaround you would look like if you could travel with nearlythespeed of light? Turn your smart phone or tablet into aspecialrelativistic simulator and watch buildings around youapparentlydeform the faster you move.The physics behind this visualization is the specialrelativisticaberration effect. The only thing you need is an imagethat coversthe full sphere (4pi sterad) in equirectangularprojection. Theinitial image shows a 4x4x4 grid. You as theobserver will always beat the center of the image but you can havedifferent velocities. Towatch only the aberration effect, load ablank white image andmodify the 'Grid strength'.