November 2013 - mathfun@mailman.xmission.com

Re: [math-fun] Newman = -1/Oldman
by Adam P. Goucher 17 Nov '13

17 Nov '13

> Fred Lunnon wrote: > > I should be much obliged if somebody would confirm or refute this conjecture, > if possible attaching relevant references. Here's one I prepared earlier: http://cp4space.wordpress.com/2013/10/24/enumerating-the-rationals/ Sincerely, Adam P. Goucher

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Re: [math-fun] Space-filling fractals in 2D and 3D
by Henry Baker 16 Nov '13

16 Nov '13

Very cool! Thanks for posting! At 06:33 PM 11/16/2013, Stuart Anderson wrote: >Here is another approach to space-filling; This is a technique of >iteratively tiling the plane with non-overlapping shapes where, on each >iteration, the position is determined randomly and the area is some >decreasing function. > >http://paulbourke.net/texture_colour/randomtile/ > >http://john-art.com/stat_geom_sampler.html > >http://john-art.com/stat_geom_linkpage.html > >Stuart

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[math-fun] Space-filling fractals in 2D and 3D
by Stuart Anderson 16 Nov '13

16 Nov '13

Here is another approach to space-filling; This is a technique of iteratively tiling the plane with non-overlapping shapes where, on each iteration, the position is determined randomly and the area is some decreasing function. http://paulbourke.net/texture_colour/randomtile/ http://john-art.com/stat_geom_sampler.html http://john-art.com/stat_geom_linkpage.html Stuart

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Re: [math-fun] But officer, they're just a little underinflated
by Henry Baker 16 Nov '13

16 Nov '13

STL comes in 2 flavors: ascii and binary. Binary uses 32-bit IEEE floats for X,Y,Z coordinates, and presumably any ascii STL file will be read-converted into internal 32-bit IEEE floats, as well. There are 2 problems with using floats for STL: writing & reading. If you've built a "watertight"/"legal" 3D model with _rational_ coordinates, the mere rounding from rational to 32-bit IEEE binary float coordinates could make the "watertight"/"legal" model into a non-watertight/illegal model due to "interference" from one portion of the model intersecting with another portion of the model. However, even if you have a "watertight"/"legal" model whose exact coordinates are specified with 32-bit IEEE binary floats, some (most?) reader(s) used to read STL files may incorrectly determine that the file isn't watertight/legal, due to _imprecision_ in the computations used to check watertightness/legality. I've been considering building an STL "writer" which is capable of "relaxing" the positions of X,Y,Z coordinates just enough to keep watertightness/legality when read by these inferior readers. However, this is a large amount of work, both the write the code and to compute the relaxation. It would be better to have "design rules" which would enable the automatic generation of always-watertight/legal STL models in the first place. I have already built an STL reader which is bit-exact. However, checking watertightness/legality in a bit-exact manner is quite computationally intensive. It is conceivable that such checking is necessarily computationally intensive, because the denominators may multiply into extremely large numbers if they are relatively prime. At 12:37 PM 11/16/2013, Bill Gosper wrote: >> For 3D stuff, "STL" format is very popular, but I don't know if >> there are any STL plugins for browsers yet. > >STL is perhaps the only pathway from Mathematica 3D polygons >to NeilBs 3Dprinterware. Mma's exporter uses an atrociously >inefficient and illegal triangulator that sorely tests Neil's patience >and skill.

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Re: [math-fun] But officer, they're just a little underinflated
by Bill Gosper 16 Nov '13

16 Nov '13

On 2013-11-16 04:26, Fred Lunnon wrote: > CDF player 245 Mb, ~10 mins to download (doesn't inform of progress), > 845 Mb on disc. Message "failed to install properly" (Safari under Mac OSX). > Ouch. > Conclusion: U/S. WFL > = Ulfram/Sux? Since the whole subtext is presumably Mathematica marketing, I doubt Wolfram is knowingly restricting cdf players to the US. Anyone else have any luck? It could be great if this worked. Especially with writing such a small file. > > > On 11/16/13, Bill Gosper <billgosper(a)gmail.com> wrote: >> You take a right turn a bit fast and get some tire squeal >> a) mostly from the left >> b) mostly from the right >> c) about equally from all four. >> --rwg I expected a), and yesterday was startled by b), prompting the veridical suspicion my right tires were underinflated. >> PS, Adobe reader is *still* trying to write that little 78.8MB .nb. >> I think Mma is telling me I'm being an idiot. >> Instead of stupid pdfs and gif vines, I should be writing, e.g., >> http://gosper.org/trilbertloopsedgescorners.cdf >> and whoever wants to actually manipulate the graphics can download >> http://www.wolfram.com/cdf-player/ . >> Only I worry that this cdf, instead of >> being 300 times larger than its notebook, is 7 times smaller. When I >> try to view it by downloading my own cdf player, I'm told that I >> already have the latest version--Mathematica 9.0.1. >> So perhaps a few of you w/o Mathematica who feel like downloading >> Wolfram's player can tell me if the three Graphics3Ds are mouse >> tumblable. They are in my "cdf previewer", but the doc says all >> interactivity must use Manipulate. >> --rwg On 2013-11-16 06:36, Henry Baker wrote: > Have you ever considered using non-Adobe pdf readers? > > I gave up on Adobe readers when they grew beyond 100MB & > incorporated all kinds of security holes & builtin spyware. > > SumatraPDF.exe is only 5.15MB. > > Ghostscript.exe is 13.5MB; a little slower, but more flexible. > > I've heard that some people use Foxit, which is about the > same size as Sumatra. > Presumably, Adobe's mistake in this case is to use an O(n^2) or worse (e.g. bubblesort) algorithm while trying to deflate Mathematica's 300fold overinflation. Does any of this other PDFware even attempt this? Apple's preview just took many minutes to further inflate from 78.8 to 160.4 MB!! > Why don't you output "SVG" (Scalable Vector Graphics) format? > > I believe that SVG now has native support in almost all browsers, > including HTML5. > > http://www.w3schools.com/svg/svg_inhtml.asp > Sounds tryworthy, if the displayed text is selectable. > For 3D stuff, "STL" format is very popular, but I don't know if > there are any STL plugins for browsers yet. > STL is perhaps the only pathway from Mathematica 3D polygons to NeilBs 3Dprinterware. Mma's exporter uses an atrociously inefficient and illegal triangulator that sorely tests Neil's patience and skill. > At 10:49 PM 11/15/2013, Bill Gosper wrote: >>PS, Adobe reader is *still* trying to write that little 78.8MB .nb. > --rwg

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Re: [math-fun] But officer, they're just a little underinflated
by Henry Baker 16 Nov '13

16 Nov '13

Have you ever considered using non-Adobe pdf readers? I gave up on Adobe readers when they grew beyond 100MB & incorporated all kinds of security holes & builtin spyware. SumatraPDF.exe is only 5.15MB. Ghostscript.exe is 13.5MB; a little slower, but more flexible. I've heard that some people use Foxit, which is about the same size as Sumatra. Why don't you output "SVG" (Scalable Vector Graphics) format? I believe that SVG now has native support in almost all browsers, including HTML5. http://www.w3schools.com/svg/svg_inhtml.asp For 3D stuff, "STL" format is very popular, but I don't know if there are any STL plugins for browsers yet. At 10:49 PM 11/15/2013, Bill Gosper wrote: >PS, Adobe reader is *still* trying to write that little 78.8MB .nb.

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[math-fun] But officer, they're just a little underinflated
by Bill Gosper 16 Nov '13

16 Nov '13

You take a right turn a bit fast and get some tire squeal a) mostly from the left b) mostly from the right c) about equally from all four. --rwg PS, Adobe reader is *still* trying to write that little 78.8MB .nb. I think Mma is telling me I'm being an idiot. Instead of stupid pdfs and gif vines, I should be writing, e.g., http://gosper.org/trilbertloopsedgescorners.cdf and whoever wants to actually manipulate the graphics can download http://www.wolfram.com/cdf-player/ . Only I worry that this cdf, instead of being 300 times larger than its notebook, is 7 times smaller. When I try to view it by downloading my own cdf player, I'm told that I already have the latest version--Mathematica 9.0.1. So perhaps a few of you w/o Mathematica who feel like downloading Wolfram's player can tell me if the three Graphics3Ds are mouse tumblable. They are in my "cdf previewer", but the doc says all interactivity must use Manipulate. --rwg

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[math-fun] hilbertish curve via gray code in radix R
by Warren D Smith 15 Nov '13

15 Nov '13

View X as an unsigned integer with <=D digits written in radix R, and also as the D-vector of those digits. The function uint gray(uint X){ return VectorSubtract(X, RightShift(X)) mod R; } converts X to a different such integer. This is a radix-R generalization of the usual binary gray code. This maps the integers which walk from 0 to R^D - 1, to D-dimensional vectors within the hypercube grid {0,1,2,...,R-1}^D which walk in hamilton-tour style via nearest neighbor steps, visiting each grid point exactly once. Extremely trivial implementation of a Hilbertish space filling curve... but it treats the different coordinates very differently, which is annoying.

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[math-fun] discontinuous rational functions & school textbooks
by Warren D Smith 15 Nov '13

15 Nov '13

It actually is possible for a rational function OF SEVERAL VARIABLES to be discontinuous. I.e. different limits as you approach a 0/0 point from different directions. Little known fact. You might want to read Feynman about his experiences re school textbooks; he was on a California board trying to decide on textbooks. He seemed to conclude it was beyond his power to correct the idiocy.

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[math-fun] Hilbert curves, Lunnon, fxt
by Warren D Smith 15 Nov '13

15 Nov '13

It looks like Lunnon did a comparatively good job re multi-D Hilbert curves on Arndt's web page. However, I still think there ought to be code much better (meaning simpler & shorter) that nobody has written yet. I don't think it is terribly hard, but it is a pain to figure out the details & get them right, and so far that pain barrier has proved sufficient to stop the code from being.

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