**Message-ID:** <Pine.NEB.4.64.0706040235470.13837@panix3.panix.com>

**From:** Alan Sondheim <sondheim@panix.com>

**To:** Cyb <cybermind@listserv.aol.com>, Wryting-L <WRYTING-L@listserv.wvu.edu>

**Subject:** Raster, symmetries, and request for help

**Date:** Mon, 4 Jun 2007 02:36:44 -0400 (EDT)

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.