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 is 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.
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
Currently available for Windows or (Intel) OSX.
The meaning and purpose of life is to give life purpose and meaning. The instigation of violence indicates a lack of spirituality.
Fractal1 { fractal: title="Fractal1" width=928 height=696 layers=6 credits="Dave Makin;6/18/2015;D J Makin;12/20/2011;Dave Makin;10/5/2\ 011;David Makin;6/15/2008;Frederik Slijkerman;7/23/2002" layer: caption="Layer 5" opacity=100 method=multipass mapping: center=-0.33275158/1.251496835 magn=0.093580419 transforms=1 transform: filename="sam.uxf" entry="SemiRegularTesselationII" p_spiral=yes p_dual=yes p_mode=Squares p_magn=1.0 p_rot=0.0 p_center=0/0 p_stab=no p_orderx=8 p_ordery=10.0 p_slope=.3 p_stabs=no formula: maxiter=100 percheck=off filename="Standard.ufm" entry="Pixel" inside: transfer=none outside: density=3 transfer=linear filename="Standard.ucl" entry="Basic" p_type=Real gradient: smooth=yes rotation=178 index=434 color=43775 index=520 color=512 index=177 color=6555392 index=241 color=13331232 index=345 color=16777197 opacity: smooth=no index=0 opacity=255 layer: caption="Layer 4" opacity=100 method=multipass mapping: center=-0.0293887315/-0.05407522515 magn=1.7360544 transforms=1 transform: filename="sam.uxf" entry="HyperbolicTilings" p_mode=Mapping p_n=3 p_k=8 p_sym="Rotation only" p_center=0/0 p_rot=0.0 p_magn=1.0 p_corrmap=yes p_niter=1000 formula: maxiter=100 percheck=off filename="Standard.ufm" entry="Pixel" inside: transfer=none outside: density=3 transfer=linear filename="Standard.ucl" entry="Basic" p_type=Real gradient: smooth=yes rotation=178 index=434 color=43775 index=520 color=512 index=177 color=6555392 index=241 color=13331232 index=345 color=16777197 opacity: smooth=no index=0 opacity=255 layer: caption="Layer 3" opacity=100 method=multipass mapping: center=1.363636372/-0.477272725 magn=0.24444444 transforms=1 transform: filename="sam.uxf" entry="AperiodicTilingIV" p_tiling0=I p_tiling2=I p_mode="All the tiles" p_center=0/0 p_rot=0.0 p_magn=1.0 p_mask=None p_invm=no p_zccenter=0/0 p_zcrot=0.0 p_zcsize=1.0 p_stab=no p_niter=10 formula: maxiter=100 percheck=off filename="Standard.ufm" entry="Pixel" inside: transfer=none outside: density=3 transfer=linear filename="Standard.ucl" entry="Basic" p_type=Real gradient: smooth=yes rotation=178 index=434 color=43775 index=520 color=512 index=177 color=6555392 index=241 color=13331232 index=345 color=16777197 opacity: smooth=no index=0 opacity=255 layer: caption="Layer 2" opacity=100 method=multipass mapping: center=1.363636372/-0.477272725 magn=0.24444444 transforms=1 transform: filename="sam.uxf" entry="Quasip3d" p_mode=Mapping p_xrot=34.0 p_yrot=34.0 p_zrot=1.0 p_center=0/0 p_rot=0.0 p_size=1.0 p_col1=0/0 p_col2=1/0 p_col3=2/0 formula: maxiter=100 percheck=off filename="Standard.ufm" entry="Pixel" inside: transfer=none outside: density=8 transfer=linear filename="Standard.ucl" entry="Basic" p_type=Real gradient: smooth=yes rotation=1 index=0 color=6555392 index=64 color=13331232 index=168 color=16777197 index=257 color=43775 index=343 color=512 opacity: smooth=no index=0 opacity=255 layer: caption="Layer 1" opacity=100 method=multipass mapping: center=1e-11/0 magn=1 transforms=1 transform: filename="sam.uxf" entry="Voroni" p_mode=Mapping p_frame=None p_psize=.5 p_tresh=1.0 p_regtile=yes p_regpar=4.0 p_center=0/0 p_rot=0.0 p_magn=1.0 p_mask=None p_minv=no p_morder=4 p_mcenter=0/0 p_mrot=0.0 p_msize=1.0 p_mr=1.0 formula: maxiter=100 percheck=off filename="Standard.ufm" entry="Pixel" inside: transfer=none outside: density=8 transfer=linear filename="Standard.ucl" entry="Basic" p_type=Real gradient: smooth=yes rotation=1 index=0 color=6555392 index=64 color=13331232 index=168 color=16777197 index=257 color=43775 index=343 color=512 opacity: smooth=no index=0 opacity=255 layer: caption="Background" opacity=100 method=multipass mapping: center=1e-11/0 magn=1 transforms=1 transform: filename="sam.uxf" entry="TFPenroseTiling" p_mode="All the tiles" p_center=0/0 p_rot=0.0 p_magn=1.0 p_mask=None p_invm=no p_zccenter=0/0 p_zcrot=0.0 p_zcsize=1.0 p_stab=no p_niter=10 formula: maxiter=100 percheck=off filename="Standard.ufm" entry="Pixel" inside: transfer=none outside: density=8 transfer=linear filename="Standard.ucl" entry="Basic" p_type=Real gradient: smooth=yes rotation=1 index=0 color=6555392 index=64 color=13331232 index=168 color=16777197 index=257 color=43775 index=343 color=512 opacity: smooth=no index=0 opacity=255 }
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