[NetBehaviour] Raster, symmetries, and request for help

[james jwm-art net]

animation illustrating increased depth of anti-aliasing:

http://www.jwm-art.net/tanned.gif




On 4/6/2007, "james jwm-art net" <james at jwm-art.net> wrote:

>anti-aliasing?
>
>
>On 4/6/2007, "Alan Sondheim" <sondheim at panix.com> wrote:
>
>>
>>
>>
>>Raster
>>
>>
>>I graph various forms of the equation y = tan(x^2); interesting phenomena
>>appear. Check out the .gif images at http://www.asondheim.org/ - the names
>>are equation00.gif, equation01.gif, etc. The graphs extend along the
>>x-axis with what appear to be constantly changing local symmetries. I have
>>experimented with different software/hardware, beginning with a TI-85
>>graphing calculator and a highly precision similar software program,
>>GraphCalc (obtained from Sourceforge). I've also used the graphing calcu-
>>lator and Mathematica in Mac OS9. Only in the last, Mathematica, did the
>>symmetries seem to disappear. I think the phenomena - the perception of
>>local symmetries - is the result of raster, i.e. the digitalization pro-
>>cess in the calculation of what are basically analogic functions. Raster
>>is tolerance-dependent; it's the digital 'jump' screened against the real.
>>The symmetries appear to be, masquerade as, independent 'things,' dif-
>>ferent from one another, lined up and sometimes intersecting in a chaotic
>>fashion. In other words, the appearance of things is constituted here by
>>the very absence of things; within the digital raster, every point, pixel,
>>is independent, disconnected, from every other.
>>
>>Ah well, it's late and I'm not expressing myself well. I'll try again:
>>Given y = tan(x^2), the resulting graph on a digital computer seems to be
>>raster-dependent; the image appears to possess local and intersecting
>>symmetrical segments which seem chaotic. These segments can be considered
>>'things' in the sense of perceptually-defined contour-mapping. (In other
>>words, they appear to be things, local processes, local phenomena, whether
>>or not they are in 'actuality,' within the real.) Using a bad metaphor,
>>such 'things' are clearly gestalt images of disconnected pixels - i.e. a
>>line in the graph which appears connected, isn't. When sections of the
>>graph are enlarged, their morphology may radically transform. So what I'm
>>interested in is the digital representation of this particular group of
>>analogic functions, and the mathematics behind it. Is the representation
>>really chaotic? Are the symmetries really geometrically different from one
>>another, and if so, what's the mathematics behind this? And so forth. Any
>>help you might give me s greatly appreciated. In the meantime, the images
>>are beautiful. Check out the gifs and jpegs at http://www.asondheim.org/ -
>>look at the 'equation' files.
>>
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