One of the coolest things I worked with in high school was the IBM IBSYS "MAP" (Macro Assembly Program), which ran on the 709/7090/704/7040. Fletcher utilized this macro facility to solve a combinatorial problem; as I understand, the generated assembly code itself was thrown away, because all of the computation was done within the macro expansion phase! Fletcher, John G. "A program to solve the pentomino problem by the recursive use of macros". CACM 8, 10 (Oct. 1965), 621-3. http://portal.acm.org/citation.cfm?id=365654&dl=GUIDE&coll=GUIDE&CFID=626489... Similar hacks have been used with the preprocessor for the C language. These hacks are far more difficult with the C preprocessor due to the constraints installed to prevent looping & stack overflows. Nevertheless, some pretty cool things can still be done. See the "Obfuscated C" home page for more info: http://www.ioccc.org/ I noticed while Googling that you can still run 7090 code on your Windoze machine, should you wish to do so: http://www.piercefuller.com/oldibm-shadow/709x.html http://www.cozx.com/~dpitts/ibm7090.html At 11:53 AM 11/12/2009, Fred lunnon wrote:
My PDF viewer did cope with the PostScript original --- after several minutes of frantic computation and memory-swapping, and the production of a 3 Mbyte file!
Many years ago, I wrote similarly booby-trapped recursive PostScript for Penrose kites-and-darts tilings. [This improved upon a more primitive earlier program, which had itself been regarded with such awe by the mainframe maintenance team that they used it to test the flatbed plotter.]
The program achieved some notoriety when a firm of toilet-paper manufacturers employed it to decorate their product. Sir Roger Penrose was not amused, and threatened to take them to court. I have no recollection of how the case was finally resolved, but it did lead at the time to a certain amount of unkind ribaldry at his expense, in connection with some rather controversial cosmological speculation.
Fred Lunnon
On 11/12/09, Mike Stay <metaweta@gmail.com> wrote:
That's much better; my pdf viewer didn't render anything but the three circles.
On Thu, Nov 12, 2009 at 10:16 AM, Henry Baker <hbaker1@pipeline.com> wrote:
It is indeed a fractal. Look more closely -- there are individual dots.
Try printing this Postscript version, which actually computes the fractal inside your printer using embedded Postscript code:
http://home.pipeline.com/~hbaker1/sigplannotices/sigcol07.ps.gz
(".gz" means "gzip"; I believe that "7-zip" can ungzip this file for you.
There is a small program called "PrintFile" which can send Postscript files on Windows to your Postscript printer.
If worst comes to worst, install Ghostscript on your computer & look at the output that way.
At 10:06 AM 11/12/2009, Mike Stay wrote:
Figure three seems wrong in this rendering--shouldn't it be a fractal?
On Thu, Nov 12, 2009 at 9:47 AM, Henry Baker <hbaker1@pipeline.com> wrote:
That was my paper!
http://home.pipeline.com/~hbaker1/sigplannotices/sigcol07.pdf
At 09:19 AM 11/12/2009, mcintosh@servidor.unam.mx wrote:
Re: [math-fun] Cube root of a complex number
somewhat tangential to the original question, Möbius transformations map three points into three points. So, why not map the three roots of the cubic into the three complex roots of unity? You only get to use the coefficients of the polynomial.
I recall a paper in an ACM journal humorously dated March 32 some years ago where someond did that; I don't remember if the solution was relevant to the present inquiry.
-- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike http://reperiendi.wordpress.com
-- Mike Stay - metaweta@gmail.com http://math.ucr.edu/~mike http://reperiendi.wordpress.com