Re: [math-fun] Weisstein's compact CF notation
<note from RWG. I can't get his picture of the pi CF as a ticker tape into this message, but his URL works. It's hard to see the defects he's complaining about, but try squinting. The mathworld version doesn't have the glitches. -- rich> Date: Fri, 4 Jan 2019 03:22:41 -0800 Subject: Re: Weisstein's compact CF notation From: Bill Gosper <billgosper@gmail.com> Julian magically responded On Fri, Jan 4, 2019 at 12:44 AM Julian Ziegler Hunts <julianj.zh@gmail.com> wrote: I can't make it do what it *should* do and export a clear 256x9 image, but I can get a 256x13 with extra whitespace or a proper 512x18. The easiest way to do this is by adding Frame->False, PixelConstrained->True, ImageSize->256|512 to the ArrayPlot, followed by either Save Selection As? http://gosper.org/cfbits.png (<1K!) ? or Export (though Export adds even more padding for some reason, so it won't go below 256x15). Julian What's magic about this is that many of my ArrayPlots looked fine on the screen, but always crummy when I saved them! Stealth wysiNwyg! On Thu, Jan 3, 2019 at 7:03 PM Bill Gosper <billgosper@gmail.com> wrote: http://mathworld.wolfram.com/PiContinuedFraction.html renders the terms in strangely Arabesque binary, presumably with the pleasantly concise ArrayPlot[Transpose@PadLeft@IntegerDigits[ContinuedFraction[?, 256], 2]] ?cfbits.png from which you can read off the four Mersenne numbers 3 7 15 1, and then 4(1+8+64) = 292. But note the hypoplastic 4 bit, even after hours of experimentation. It is maddeningly difficult to prevent Mathematica, when you try to export a graphic, from blurring, rounding, stretching, shrinking, or outright amputating pixels, presumably due to premature quantization. Or incompetent DWIMmery. ?rwg Julian seems to be the only one who knows how to prevent it, and he just went back to UCLA. Eric seems to have achieved vertical fidelity, but just past the middle seems to be a double 57, which is what sucked me into this: ?rwg
For what it's worth, I had my own try at binary-plotting 2^10 continued fraction terms: http://chesswanks.com/num/CFPi1024BinaryPlot.png If your browser shrinks images to fit the window, click on the far left part of it to expand it to full size. Then scroll to the right.
Eric fixed it already! (The original predated the ArrayPlot capability.) Nice plot, Hans! —rwg On 2019-01-06 10:25, rcs@xmission.com wrote:
<note from RWG. I can't get his picture of the pi CF as a ticker tape into this message, but his URL works. It's hard to see the defects he's complaining about, but try squinting. The mathworld version doesn't have the glitches. -- rich>
Date: Fri, 4 Jan 2019 03:22:41 -0800 Subject: Re: Weisstein's compact CF notation From: Bill Gosper <billgosper@gmail.com>
Julian magically responded On Fri, Jan 4, 2019 at 12:44 AM Julian Ziegler Hunts <julianj.zh@gmail.com> wrote:
I can't make it do what it *should* do and export a clear 256x9 image, but I can get a 256x13 with extra whitespace or a proper 512x18. The easiest way to do this is by adding Frame->False, PixelConstrained->True, ImageSize->256|512 to the ArrayPlot, followed by either Save Selection As?
http://gosper.org/cfbits.png (<1K!) ? or Export (though Export adds even more padding for some reason, so it won't go below 256x15). Julian What's magic about this is that many of my ArrayPlots looked fine on the screen, but always crummy when I saved them! Stealth wysiNwyg!
On Thu, Jan 3, 2019 at 7:03 PM Bill Gosper <billgosper@gmail.com> wrote:
http://mathworld.wolfram.com/PiContinuedFraction.html renders the terms in strangely Arabesque binary, presumably with the pleasantly concise ArrayPlot[Transpose@PadLeft@IntegerDigits[ContinuedFraction[?, 256], 2]]
?cfbits.png from which you can read off the four Mersenne numbers 3 7 15 1, and then 4(1+8+64) = 292. But note the hypoplastic 4 bit, even after hours of experimentation. It is maddeningly difficult to prevent Mathematica, when you try to export a graphic, from blurring, rounding, stretching, shrinking, or outright amputating pixels, presumably due to premature quantization.
Or incompetent DWIMmery. ?rwg
Julian seems to be the only one who knows how to prevent it, and he just went back to UCLA. Eric seems to have achieved vertical fidelity, but just past the middle seems to be a double 57, which is what sucked me into this: ?rwg
_______________________________________________ math-fun mailing list math-fun@mailman.xmission.com https://mailman.xmission.com/cgi-bin/mailman/listinfo/math-fun
participants (3)
-
Hans Havermann -
rcs＠xmission.com -
rwg