Re: [math-fun] DIY penrose shower floor
Questions: Exactly what happens to the iso"perimetric" quotient when you delete the interior faces of a Weaire-Phelan unit cell? (For all distinguishable translations.) What is the exact, analytic quotient for Kelvin's cell? (The ISCs don't even recognize 64*π/3/(1 + 2*Sqrt[3])^3.) (Shudder) ditto for the Weaire-Phelan? --rwg On 2015-06-10 18:37, James Propp wrote:
Where do things stand now? Is it still possible to get pseudo-aperiodic toilet paper?
And while we're on the subject: do Weaire and Phelan have any kind of copyright on the Weaire-Phelan structure that they discovered (subsequently incorporated into the Water Cube in Beijing)?
Jim Propp
On Wed, Jun 10, 2015 at 8:48 PM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
I regret to have to confess was the culprit responsible for designing the modified tiling (periodic along one axis) --- ah --- behind this particular contribution to the artistic life of the twentieth century.
Not for the first or last time, I failed received so much as a letter of thanks from the commercial enterprise concerned. [Though I was subsequently obliged to --- er --- come clean to Penrose about my part in the affair.]
Moral: if you are approached by an individual with an enquiry of a suspiciously industrial nature, get things --- um --- down on paper beforehand!
Fred Lunnon
On 6/11/15, James Propp <jamespropp@gmail.com> wrote:
Was all the Penrose tiling toilet paper manufactured by Kimberly Clark in the late 90s destroyed, or does some of it still survive?
If there are still rolls out there, and the price isn't prohibitive, you could install some (presumably for display purposes only) elsewhere in the bathroom.
If you don't know[ꞥ] the story of Sir Roger's lawsuit against Kimberly Clark, I urge you to look it up. It features one especially memorable quote, from David Bradley: "When it comes to the population of Great Britain being invited by a multinational to wipe their bottoms on what appears to be a work of a knight of the realm without his permission, then a last stand must be made."
Jim Propp
On Wednesday, June 10, 2015, Dirk Lattermann <dlatt@alqualonde.de> wrote:
Finally, a year after we moved into our new (old) house, I managed to finish the penrose mosaic for the shower in our ground floor bathroom.
I put two quick pictures, before the glass wall was installed, at
http://folgenschwer.de/mosaik/
Thought some of you might enjoy, Dirk
On 2015-06-12 13:30, Bill Gosper wrote:
Questions: Exactly what happens to the iso"perimetric" quotient when you delete the interior faces of a Weaire-Phelan unit cell? (For all distinguishable translations.) What is the exact, analytic quotient for Kelvin's cell? (The ISCs don't even recognize 64*π/3/(1 + 2*Sqrt[3])^3.) (Shudder) ditto for the Weaire-Phelan? --rwg
Wow, no takers. I bet it's a toughie. Anyway, I was lucky enough to visit Nathan Myrhvold's superhouse, which is wall-to-wall aperiodic, waterjetted from large slabs of semiprecious minerals, except glass where you can look down at the indoor pool. Floor to ceiling, the walls are aperiodic wooden lattices and panels. Need I describe the ceilings? Indeed, even the bathroom drain grates. (As George suggested. But unsymmetrical. The tilings are all original.) And the huge metal gate and inner door, and the rolling gate at the street,... Jennifer Chayes calls it a grand mosque. Nathan calls it the house that Mathematica built. Visiting Stephen Wolfram sniffed, "Well, I live in the house that Mathematica *paid for*." --rwg
On 2015-06-10 18:37, James Propp wrote:
Where do things stand now? Is it still possible to get pseudo-aperiodic toilet paper?
And while we're on the subject: do Weaire and Phelan have any kind of copyright on the Weaire-Phelan structure that they discovered (subsequently incorporated into the Water Cube in Beijing)?
Jim Propp
On Wed, Jun 10, 2015 at 8:48 PM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
I regret to have to confess was the culprit responsible for designing the modified tiling (periodic along one axis) --- ah --- behind this particular contribution to the artistic life of the twentieth century.
Not for the first or last time, I failed received so much as a letter of thanks from the commercial enterprise concerned. [Though I was subsequently obliged to --- er --- come clean to Penrose about my part in the affair.]
Moral: if you are approached by an individual with an enquiry of a suspiciously industrial nature, get things --- um --- down on paper beforehand!
Fred Lunnon
On 6/11/15, James Propp <jamespropp@gmail.com> wrote:
Was all the Penrose tiling toilet paper manufactured by Kimberly Clark in the late 90s destroyed, or does some of it still survive?
If there are still rolls out there, and the price isn't prohibitive, you could install some (presumably for display purposes only) elsewhere in the bathroom.
If you don't know[ꞥ] the story of Sir Roger's lawsuit against Kimberly Clark, I urge you to look it up. It features one especially memorable quote, from David Bradley: "When it comes to the population of Great Britain being invited by a multinational to wipe their bottoms on what appears to be a work of a knight of the realm without his permission, then a last stand must be made."
Jim Propp
On Wednesday, June 10, 2015, Dirk Lattermann <dlatt@alqualonde.de> wrote:
Finally, a year after we moved into our new (old) house, I managed to finish the penrose mosaic for the shower in our ground floor bathroom.
I put two quick pictures, before the glass wall was installed, at
http://folgenschwer.de/mosaik/
Thought some of you might enjoy, Dirk
math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Does Weaire-Phelan refer to the curved-face shape that is the closest known solution to the problem I assume is: ----- Find a lattice on R^3 and a fundamental domain D of unit volume such that its area is minimized over all possible lattices and fundamental domains? ----- Or to the polyhedralization of same? —Dan P.S. Is it known that an absolute minimum exists?
Questions: Exactly what happens to the iso"perimetric" quotient when you delete the interior faces of a Weaire-Phelan unit cell? (For all distinguishable translations.) What is the exact, analytic quotient for Kelvin's cell? (The ISCs don't even recognize 64*π/3/(1 + 2*Sqrt[3])^3.) (Shudder) ditto for the Weaire-Phelan?
I have 49 aperiodic tilings in the house, many of which were not physically realized until I made them. A couple I came up with myself. I also have the first (to my knowledge) aperiodic parquet deformation - a continuous transformation of one aperiodic tiling into another. It is on the walls of a room and wraps around the deformation parameter. Nathan
-----Original Message----- From: rwg [mailto:rwg@sdf.org] Sent: Saturday, June 13, 2015 2:06 PM To: math-fun Subject: Re: [math-fun] DIY penrose shower floor
On 2015-06-12 13:30, Bill Gosper wrote:
Questions: Exactly what happens to the iso"perimetric" quotient when you delete the interior faces of a Weaire-Phelan unit cell? (For all distinguishable translations.) What is the exact, analytic quotient for Kelvin's cell? (The ISCs don't even recognize 64*π/3/(1 + 2*Sqrt[3])^3.) (Shudder) ditto for the Weaire-Phelan? --rwg
Wow, no takers. I bet it's a toughie. Anyway, I was lucky enough to visit Nathan Myrhvold's superhouse, which is wall-to-wall aperiodic, waterjetted from large slabs of semiprecious minerals, except glass where you can look down at the indoor pool. Floor to ceiling, the walls are aperiodic wooden lattices and panels. Need I describe the ceilings? Indeed, even the bathroom drain grates. (As George suggested. But unsymmetrical. The tilings are all original.) And the huge metal gate and inner door, and the rolling gate at the street,... Jennifer Chayes calls it a grand mosque. Nathan calls it the house that Mathematica built. Visiting Stephen Wolfram sniffed, "Well, I live in the house that Mathematica *paid for*." --rwg
On 2015-06-10 18:37, James Propp wrote:
Where do things stand now? Is it still possible to get pseudo-aperiodic toilet paper?
And while we're on the subject: do Weaire and Phelan have any kind of copyright on the Weaire-Phelan structure that they discovered (subsequently incorporated into the Water Cube in Beijing)?
Jim Propp
On Wed, Jun 10, 2015 at 8:48 PM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
I regret to have to confess was the culprit responsible for designing the modified tiling (periodic along one axis) --- ah --- behind this particular contribution to the artistic life of the twentieth century.
Not for the first or last time, I failed received so much as a letter of thanks from the commercial enterprise concerned. [Though I was subsequently obliged to --- er --- come clean to Penrose about my part in the affair.]
Moral: if you are approached by an individual with an enquiry of a suspiciously industrial nature, get things --- um --- down on paper beforehand!
Fred Lunnon
On 6/11/15, James Propp <jamespropp@gmail.com> wrote:
Was all the Penrose tiling toilet paper manufactured by Kimberly Clark in the late 90s destroyed, or does some of it still survive?
If there are still rolls out there, and the price isn't prohibitive, you could install some (presumably for display purposes only) elsewhere in the bathroom.
If you don't know[ꞥ] the story of Sir Roger's lawsuit against Kimberly Clark, I urge you to look it up. It features one especially memorable quote, from David Bradley: "When it comes to the population of Great Britain being invited by a multinational to wipe their bottoms on what appears to be a work of a knight of the realm without his permission, then a last stand must be made."
Jim Propp
On Wednesday, June 10, 2015, Dirk Lattermann
<dlatt@alqualonde.de>
wrote:
Finally, a year after we moved into our new (old) house, I managed to finish the penrose mosaic for the shower in our ground
floor bathroom.
I put two quick pictures, before the glass wall was installed, at
http://folgenschwer.de/mosaik/
Thought some of you might enjoy, Dirk
math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
But since they are presumably finite, how can you be sure they won't eventually repeat? —Dan, not being 100% serious
On Jun 16, 2015, at 11:57 AM, Nathan Myhrvold <nathanm@intven.com> wrote:
I have 49 aperiodic tilings in the house, many of which were not physically realized until I made them. A couple I came up with myself.
I also have the first (to my knowledge) aperiodic parquet deformation - a continuous transformation of one aperiodic tiling into another. It is on the walls of a room and wraps around the deformation parameter.
Nathan
How about an online picture gallery? WFL On 6/16/15, Nathan Myhrvold <nathanm@intven.com> wrote:
I have 49 aperiodic tilings in the house, many of which were not physically realized until I made them. A couple I came up with myself.
I also have the first (to my knowledge) aperiodic parquet deformation - a continuous transformation of one aperiodic tiling into another. It is on the walls of a room and wraps around the deformation parameter.
Nathan
-----Original Message----- From: rwg [mailto:rwg@sdf.org] Sent: Saturday, June 13, 2015 2:06 PM To: math-fun Subject: Re: [math-fun] DIY penrose shower floor
On 2015-06-12 13:30, Bill Gosper wrote:
Questions: Exactly what happens to the iso"perimetric" quotient when you delete the interior faces of a Weaire-Phelan unit cell? (For all distinguishable translations.) What is the exact, analytic quotient for Kelvin's cell? (The ISCs don't even recognize 64*π/3/(1 + 2*Sqrt[3])^3.) (Shudder) ditto for the Weaire-Phelan? --rwg
Wow, no takers. I bet it's a toughie. Anyway, I was lucky enough to visit Nathan Myrhvold's superhouse, which is wall-to-wall aperiodic, waterjetted from large slabs of semiprecious minerals, except glass where you can look down at the indoor pool. Floor to ceiling, the walls are aperiodic wooden lattices and panels. Need I describe the ceilings? Indeed, even the bathroom drain grates. (As George suggested. But unsymmetrical. The tilings are all original.) And the huge metal gate and inner door, and the rolling gate at the street,... Jennifer Chayes calls it a grand mosque. Nathan calls it the house that Mathematica built. Visiting Stephen Wolfram sniffed, "Well, I live in the house that Mathematica *paid for*." --rwg
On 2015-06-10 18:37, James Propp wrote:
Where do things stand now? Is it still possible to get pseudo-aperiodic toilet paper?
And while we're on the subject: do Weaire and Phelan have any kind of copyright on the Weaire-Phelan structure that they discovered (subsequently incorporated into the Water Cube in Beijing)?
Jim Propp
On Wed, Jun 10, 2015 at 8:48 PM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
I regret to have to confess was the culprit responsible for designing the modified tiling (periodic along one axis) --- ah --- behind this particular contribution to the artistic life of the twentieth century.
Not for the first or last time, I failed received so much as a letter of thanks from the commercial enterprise concerned. [Though I was subsequently obliged to --- er --- come clean to Penrose about my part in the affair.]
Moral: if you are approached by an individual with an enquiry of a suspiciously industrial nature, get things --- um --- down on paper beforehand!
Fred Lunnon
On 6/11/15, James Propp <jamespropp@gmail.com> wrote:
Was all the Penrose tiling toilet paper manufactured by Kimberly Clark in the late 90s destroyed, or does some of it still survive?
If there are still rolls out there, and the price isn't prohibitive, you could install some (presumably for display purposes only) elsewhere in the bathroom.
If you don't know[ꞥ] the story of Sir Roger's lawsuit against Kimberly Clark, I urge you to look it up. It features one especially memorable quote, from David Bradley: "When it comes to the population of Great Britain being invited by a multinational to wipe their bottoms on what appears to be a work of a knight of the realm without his permission, then a last stand must be made."
Jim Propp
On Wednesday, June 10, 2015, Dirk Lattermann
<dlatt@alqualonde.de>
wrote:
> Finally, a year after we moved into our new (old) house, I > managed to finish the penrose mosaic for the shower in our ground
floor bathroom.
> > I put two quick pictures, before the glass wall was installed, at > > http://folgenschwer.de/mosaik/ > > Thought some of you might enjoy, > Dirk >
math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
Fred, Dan, Nathan's not a subscriber. You must include his email address in the To or Cc lines if you want the message to reach him. I've set the permissions so that any reply he makes to the list will go through. --Rich ------ Quoting Fred Lunnon <fred.lunnon@gmail.com>:
How about an online picture gallery? WFL
On 6/16/15, Nathan Myhrvold <nathanm@intven.com> wrote:
I have 49 aperiodic tilings in the house, many of which were not physically realized until I made them. A couple I came up with myself.
I also have the first (to my knowledge) aperiodic parquet deformation - a continuous transformation of one aperiodic tiling into another. It is on the walls of a room and wraps around the deformation parameter.
Nathan
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. http://www.ultrafractal.com/ 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 }
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 }
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
On 18 Jun 2015, at 22:24, rwg wrote:
And if those arcs were actually quarter-circles, they could tangentially co-rotate in a "pumping wall". Has nobody made a gif? --rwg
Not that I know of - but I wouldn't be at all surprised if someone has. The methods for the recent 3D fractal (2009+) creation the "Mandelbox" also allow the creation of interesting and complex patterns, though generally finite in nature rather than full tilings. Examples using my own colouring formula for UF (mmf5.ucl:Folded Patterns): http://makinmagic.deviantart.com/art/I-ain-t-afraid-of-no-ghost-278588866 http://makinmagic.deviantart.com/art/In-the-Palace-278173851 http://makinmagic.deviantart.com/art/It-s-in-the-blood-278035502 In case anyone's not seen any of the original "Mandelbox"es: http://makinmagic.deviantart.com/art/Pandora-s-Box-159750639 bye Dave The meaning and purpose of life is to give life purpose and meaning. The instigation of violence indicates a lack of spirituality.
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 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
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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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[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
I’m sure math-funsters will be interested to hear that Roger Penrose, age 83 and three quarters, is to present a BBC documentary about Escher - impossible staircases, tilings, etc. It is shooting over the next couple of months, and will presumably be broadcast towards the end of the year.
On 16 Jun 2015, at 19:57, Nathan Myhrvold <nathanm@intven.com> wrote:
I have 49 aperiodic tilings in the house, many of which were not physically realized until I made them. A couple I came up with myself.
I also have the first (to my knowledge) aperiodic parquet deformation - a continuous transformation of one aperiodic tiling into another. It is on the walls of a room and wraps around the deformation parameter.
Nathan
-----Original Message----- From: rwg [mailto:rwg@sdf.org] Sent: Saturday, June 13, 2015 2:06 PM To: math-fun Subject: Re: [math-fun] DIY penrose shower floor
On 2015-06-12 13:30, Bill Gosper wrote:
Questions: Exactly what happens to the iso"perimetric" quotient when you delete the interior faces of a Weaire-Phelan unit cell? (For all distinguishable translations.) What is the exact, analytic quotient for Kelvin's cell? (The ISCs don't even recognize 64*π/3/(1 + 2*Sqrt[3])^3.) (Shudder) ditto for the Weaire-Phelan? --rwg
Wow, no takers. I bet it's a toughie. Anyway, I was lucky enough to visit Nathan Myrhvold's superhouse, which is wall-to-wall aperiodic, waterjetted from large slabs of semiprecious minerals, except glass where you can look down at the indoor pool. Floor to ceiling, the walls are aperiodic wooden lattices and panels. Need I describe the ceilings? Indeed, even the bathroom drain grates. (As George suggested. But unsymmetrical. The tilings are all original.) And the huge metal gate and inner door, and the rolling gate at the street,... Jennifer Chayes calls it a grand mosque. Nathan calls it the house that Mathematica built. Visiting Stephen Wolfram sniffed, "Well, I live in the house that Mathematica *paid for*." --rwg
On 2015-06-10 18:37, James Propp wrote:
Where do things stand now? Is it still possible to get pseudo-aperiodic toilet paper?
And while we're on the subject: do Weaire and Phelan have any kind of copyright on the Weaire-Phelan structure that they discovered (subsequently incorporated into the Water Cube in Beijing)?
Jim Propp
On Wed, Jun 10, 2015 at 8:48 PM, Fred Lunnon <fred.lunnon@gmail.com> wrote:
I regret to have to confess was the culprit responsible for designing the modified tiling (periodic along one axis) --- ah --- behind this particular contribution to the artistic life of the twentieth century.
Not for the first or last time, I failed received so much as a letter of thanks from the commercial enterprise concerned. [Though I was subsequently obliged to --- er --- come clean to Penrose about my part in the affair.]
Moral: if you are approached by an individual with an enquiry of a suspiciously industrial nature, get things --- um --- down on paper beforehand!
Fred Lunnon
On 6/11/15, James Propp <jamespropp@gmail.com> wrote:
Was all the Penrose tiling toilet paper manufactured by Kimberly Clark in the late 90s destroyed, or does some of it still survive?
If there are still rolls out there, and the price isn't prohibitive, you could install some (presumably for display purposes only) elsewhere in the bathroom.
If you don't know[ꞥ] the story of Sir Roger's lawsuit against Kimberly Clark, I urge you to look it up. It features one especially memorable quote, from David Bradley: "When it comes to the population of Great Britain being invited by a multinational to wipe their bottoms on what appears to be a work of a knight of the realm without his permission, then a last stand must be made."
Jim Propp
On Wednesday, June 10, 2015, Dirk Lattermann
<dlatt@alqualonde.de>
wrote:
> Finally, a year after we moved into our new (old) house, I > managed to finish the penrose mosaic for the shower in our ground
floor bathroom.
> > I put two quick pictures, before the glass wall was installed, at > > http://folgenschwer.de/mosaik/ > > Thought some of you might enjoy, > Dirk >
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participants (8)
-
Alex Bellos -
Bill Gosper -
Dan Asimov -
David Makin -
Fred Lunnon -
Nathan Myhrvold -
rcs＠xmission.com -
rwg