[NetBehaviour] Raster, symmetries, and request for help

[james jwm-art net]

anti-aliasing?


On 4/6/2007, "Alan Sondheim" <sondheim at panix.com> wrote:

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>Raster
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>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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