I'm intrigued by Jack Holloway's recursive pentagram snowflake design, Fig 31 in the Minskys & Trinskys book<http://www.blurb.com/bookstore/detail/2172660>. However, circularizing and sampling obscure the pixel structure, and how, if at all, it relates to Fig 30. As usual, Julian comes to the rescue, with a "period 5" trinsky in which orbital x+y stays constant mod 2. The "black squares" (checkerboard) subset of this bitmap strongly resembles Fig 31, except the bounding pentagons have vertex angles of π/2 and 3π/4 instead of 3π/5. So I linearly crunched it to have "rhombic pixels" and wrote http://www.tweedledum.com/rwg/rhombicp5.svg The .svg is so you can scale it up without antialiasing. Unfortunately, my Apple Firefox scales it right off the screen, and refuses to scroll it back! Safari scrolls, but won't let you zoom very far. And Preview won't load svgs at all! And, as of this AM, gosper.org delivers source text instead of graphics for it. So to mega zoom it, Neil suggested downloading inkscape<http://inkscape.org/>, which seems to work great. Can one speak of the limit of this pattern in the large? The pentagram outlines grow without bound and get "infinitely thin", yet seem to fill space. And what is a formula for their limiting shape? Julian (quoted without permission) explains the original image as follows: (d_t means the trinsky d multiplier, etc.) It's the Trinsky equivalent of p5d1, which is d=g=1, e=2*sin^2(π/5). The Minsky-Trinsky equivalence is has d_t=g_t=d_m, e_t=e_m/2, has x about twice as large to compensate. This is what causes the checkerboarded images–for a given Trinsky (x,y), the equivalent Minsky point is ((x+⸤d_t*y⸥)/2,y) (sorry about the floors I haven't found any decent floor characters to use), and the checkerboard pattern comes from whether (x+⸤d_t*y⸥)/2 is an integer or not. The "checkerboard" pattern is only when the Trinksy d=g=1, in which case x+y is constant mod 2: x'=x-y=c mod 2, y'=y+⸤e*x⸥, x''=x'-y'=c-y' mod 2. A granularity of 1/2 would not produce checkerboarded images–it would produce four normal (i.e. at coordinates (ax+b,cy+d)) images (or two, alternating in either columns or row but not both, if only one granularity=1/2). --rwg