THE MAD TURING'S MAZE
The MAD Computer Program is a BASIC program originally published in MAD magazine No. 258 from October 1985 that renders the MAD logo, Alfred E. Neuman’s face, and Alfred E. Neuman’s motto, “What, me worry?”. This article recounts the labyrinthine journey taken to convert the MAD Computer Program into a Turing’s Maze. The result requires only about a minute of emulation on a 5½-year-old desktop PC to generate the output:
Click on either image to view a full-resolution version (9,799 × 11,717 pixels). The maze file is available here.
To produce the logo and face, the MAD Computer Program draws 522 line segments. It renders thick lines by plotting pairs of horizontally adjacent pixels rather than single pixels. And once done with the logo and face, it prints the motto beneath them.
The conversion contains a 256×256 pixel display, the coordinates of the pixels comprising the motto, a line drawer circuit, and the endpoint coordinates of the line segments:
As revealed in the high-level diagram below, the line drawer depends on an adder-subtractor and an equality comparator, demultiplexers drive the display, and everything shares an 8-bit bus.
The maze stores the endpoint coordinates and the motto pixel coordinates in a grid of empty and buffered-filled cells, which represent logic zeros and logic ones, respectively. The grid acts as a purely sequential microprogram. As the mouse visits the cells west-to-east and south-to-north, it transfers values into the 8-bit bus and control lines in a specific order, operating the display and the line drawer.
Here is a zoom-up of part of the endpoint coordinates grid:
The motto cells encode 5×7 pixel glyphs from the Signetics 2513 character generator chip, which is used in the Apple II, the platform graphics designer Lauretta Jones created the logo and face on, and the first of four of which the magazine article provides BASIC dialect ports, the others being the Atari 8-bit family, the Commodore 64/128, and the IBM PC.
The adder-subtractor is a truncated version of the one employed by the Mandelbrot set maze. It processes 8-bit values instead of 16-bit values:
The maze could determine if two 8-bit values match by subtracting them and passing their difference to an 8-input NAND gate that checks for zero. But, for performance, the maze employs a dedicated equality comparator circuit that channels input-bit pairs into XNOR gates whose outputs combine through an 8-input AND gate:
The line drawer contains ten 8-bit registers:
|X0||First endpoint x-coordinate|
|Y0||First endpoint y-coordinate|
|X1||Second endpoint x-coordinate|
|Y1||Second endpoint y-coordinate|
|DX||Line segment run|
|DY||Line segment rise|
|SX||Step in x-direction|
|SY||Step in y-direction|
|E||Integer incremental error|
|E2||Twice the error|
The line drawer’s registers and microprogram are labeled in the image below. Note: E2 is wired such that a read performs a left-shift by 1, doubling the value on the bus.
The microprogram implements Bresenham's line algorithm:
DX ← X1 − X0 if DX7 = 1 then DX ← 0 − DX SX ← −1 else SX ← 1 end DY ← Y1 − Y0 if DY7 = 1 then SY ← −1 else DY ← 0 − DY SY ← 1 end E ← DX + DY while true do plot(X0, Y0) plot(X0 + 1, Y0) if X0 = X1 then if Y0 = Y1 then break end end E2 ← E << 1 if (E2 − DY)7 = 0 then if X0 = X1 then break end E ← E + DY X0 ← X0 + SX end if (DX − E2)7 = 0 then if Y0 = Y1 then break end E ← E + DX Y0 ← Y0 + SY end end
The line drawer plots a point by toggling a dichromatic cell of a 256×256 matrix from green to red. The image below depicts a 4×4 submatrix of the display.
The display resembles the one in the Mandelbrot set maze, except the color scheme is inverted and the cells are twice the size.
The MAD Computer Program, the MAD logo, and Alfred E. Neuman’s face and motto are the copyrighted, intellectual property of E.C. Publications, Inc., a subsidiary of DC Entertainment, a subsidiary of Warner Bros. Discovery. But the magazine instructs their loyal readers to, “Enter into your computer the program below and create your own MAD logo and Alfred E. Neuman face!” It goes on to demand physical reproductions by “calling for a printout”. It even directs readers to mail them paper copies. The author of this page is not affiliated with or endorsed by them. Please don't sue me!
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