Gallery
Here are some images written using pq-png. They are 256 pixels in width and height. Their captions show the painter and q-value used to paint them.
PQ images are a kind of mathematical art. I discovered them around 2019.
These programs and libraries are part of Misk. I use pq-fb to explore the images and pq-png to save them.
In a PQ image, a function of the form p#(q, (x, y)) is applied to every pixel. The #, q, x, y, and output of the function are nonnegative integers. The function is called a painter. The # is called the identifier (ID). The q is called the q-value. The x and y are the horizontal and vertical coordinates of a pixel, respectively. Pixel (x, y) is black if p#(q, (x, y)) = 0, otherwise it is white.
For pixel (x, y), the pixel to its right is at (x + 1, y), and the pixel below it is at (x, y + 1). The top-left pixel is at (x0, y0), where x0 and y0 are nonnegative integers called x-offset and y-offset, respectively. Pixel (0, 0) is called the origin.
There are 50 defined painters, 0 through 49, divided into 10 classes, 0 through 9. Painters in odd classes divide by q, so q = 0 is undefined for them. For all painters, p#(q, (x, y)) = p#(q, (y, x)).
The following is a list of all painters, where & denotes bitwise AND, | denotes bitwise inclusive OR, ^ denotes bitwise exclusive OR, * denotes multiplication, which has the highest precedence, and % denotes modulo:
For a PQ image with width 3, height 2, x-offset x0 = 1, and y-offset y0 = 2, the pixels of the image are numbered as follows:
| (1, 2) | (2, 2) | (3, 2) |
| (1, 3) | (2, 3) | (3, 3) |
Painter 8 with q-value 4 is applied to every pixel as follows:
The pixels are colored as follows:
| White | Black | White |
| Black | White | White |
Pixel (2, 2) is black because p8(4, (2, 2)) = 0. Pixel (1, 2) is white because p8(4, (1, 2)) ≠ 0.
Here is an interactive demo of PQ images. From the options below, select a painter and input the q-value to paint the canvas. Note that the options are limited in comparison with those of the main program: pq-png.
| Program | Painter | Length | Offset |
|---|---|---|---|
| Demo | 2 or 42 | 256 | 0 |
| Main | 0 to 49 | 1 to 215 | 0 to 232 - 1 |
Here are some images written using pq-png. They are 256 pixels in width and height. Their captions show the painter and q-value used to paint them.