XY Images

Software

• xy-png - write an XY image to a PNG file

This program is part of Misk.

Definition

Let positive integers w and h be the width and height of an XY image, in pixels, respectively. Let X and Y be the sets of nonnegative integers less than w and h, respectively. Let P be the set of products of multiplying every element of X by every element of Y. Number the pixels of the image 0, 1, 2, and so on from top to bottom and left to right. A pixel is black if its number is in P, otherwise it is white.

Example

For the XY image with width w = 3 and height h = 2, the sets defined above become:

• X = {0, 1, 2}
• Y = {0, 1}
• P = {0 × 0, 0 × 1, 1 × 0, 1 × 1, 2 × 0, 2 × 1} = {0, 1, 2}

The pixels of the image are numbered as follows:

And colored as follows:

Pixel 0 is black because 0 is in P. Pixel 3 is white because 3 is not in P.

Observations

• The top row is black if w = h = 1 or h > 1.
• The bottom row is white if h > 1.
• Flood-filling the top row reveals shapes that I call stalactites.