[Sorry for previous no-op. Roundcube sent my reply just as I started to type it!] On 2015-06-18 14:24, rwg wrote:
On 2015-06-18 08:38, David Makin wrote:
Hi all,
Nice real renditions there, for anyone wanting short-cuts to visualising tilings of various types Samuel Monnier has written several tiling transforms for Ultra Fractal.
Below [was] a standard parameter file which will render in UF provided you have the updated formula collection (which is downloadable via Ultra Fractal) - it includes several layers of Sam's transforms which include kite and dart, truchet and voronoi among others.
Hope it's of interest.
bye Dave
PS. UF is "free" for 30 days and will still work after that period but unless registered images can't be saved.
rwg> I suspect that the quadruply unshaded vertices of Kerry Mitchell's
http://www.ultrafractal.com/showcase/kerry/ghost.jpg coincide with the Hilbert quadruple points, e.g., (Julian's)
In[692]:= unbert[1/2 + I/4]
Out[692]= {5/48, 7/48, 41/48, 43/48}
Check, using my old Hilbert:
In[693]:= Hilbert /@ %
Out[693]= {1/2 + I/4, 1/2 + I/4, 1/2 + I/4, 1/2 + I/4}
And if those arcs were actually quarter-circles, they could tangentially co-rotate in a "pumping wall". Has nobody made a gif? --rwg
I meant a sheet of these things: http://toobnix.org/?p=741 Adding just two more rotors will pump another blobstream (in the opposite phase). Puzzle: Shew that the sum of the two blobstreams has constant dVolume/dt. I.e., the sum of the cross- sectional areas of the two phases always equals the quadricuspid area of the disk minus four lemons. For large n, you get n blobstreams for n+sqrt(n) rotors. Well, n + c sqrt(n) for some smallish c. --rwg