Another in my series of distance function videos.
Click the blue title to see it bigger, with explanation, on Vimeo.
10 particles move linearly at constant, random speeds, bouncing off the frame edges. For each pixel, calculate the Lp distance from the pixel to each particle, where p varies smoothly and monotonically from 1 at the start of the video to 10 at the end. Order this set of distances: d0, d1, d2, ... . Calculate the differences d1-d0, d2-d1, etc. Color the pixel a gray which is an increasing function of the smallest difference.
Made with Processing (processing.org).
Click to embiggen.
distance function: L1 distance, difference of the differences between two smallest pairs of distancesSun, 2013-03-31 19:29
180 particles move linearly at various constant speeds, in randomly chosen directions. For each pixel, determine the set of distances from the pixel to each particle. Sort this set: say the result is d0,d1,d2,... in order. Then let k=(d2-d1)-(d1-d0). Color the pixel based on an increasing function of k.
Made with processing (processing.org).
Click through for bigger on Vimeo.
New distance function video.
Thirty particles move linearly at various constant speeds, in randomly chosen directions. For each pixel, determine the set of distances from the pixel to each particle. Sort this set. Find the smallest distance in that set which is greater than the sum of the two smallest distances. Color the pixel a grey color determined by a non-decreasing function of distance.
Made with Processing ( processing.org ).
Click through to embiggen.
I made this new, higher resolution version of one of my favorite videos. I am still surprised and mystified by the complexity in it.
Click to embiggen on Vimeo.