On 2016-08-31 16:55, Bill Gosper wrote: Hi Vitaliy, I have a sandbox with a general Fourier animator. It takes a formula for the coefficients (amplitudes and phases as functions of frequency), speed, and coloration. It isn't very fast because it colors one pixel at a time, emulating the Symbolics mathematically correct draw-triangle ALU-add microcode necessary for smoothly drawing moving edges. Mathematically correct means that, if two triangles share an edge, there will never be missing or overwritten pixels, and if the triangle is "inside out", the "bump" will be negated. (The trick is to consistently define exactly which pixels to bump.) With this primitive, you can then animate the movement of an edge segment simply by drawing two triangles filling the quadrilateral defined by the old and new positions of its endpoints. To draw a seamless T joint, just [include] the "zero area" triangle formed by the constituent edges, which will usually add or subtract the "bump" constant to or from a few pixels. --Bill Howard Cannon has implemented a fast, full-res re-creation of the Symbolics triangle primitive, along with several lovely Ptolemaic sweeps, plus luxurious controls: http://hichacks.is-a-geek.net/triangles/artcircle E.g., for a nice picture of 2D Gibbs ringing, change the "Circle" box to Gibbs Tri, and click >. Besser illustrates frequency (over)modulation. The vector sum runs back and forth <Amplitude> radians along the circumference of the circle Howard (hic@iname.com) tailored the page for Chrome, and seeks your comments and suggestions. (I'll try to supply him with the coefficients for Julian's sextuple point spacefill.) --rwg