The radix is the number of unique digits, including the digit zero, used to represent numbers in a positional numeral system. The most popular of these is binary, or 2 numbers. This yields a string of zeros and ones. For example, 01010101. The natural way we think about numbers is with a radix of 10, where we have 0,1,2,3,4,5,6,7,8,9 at our disposal.
Below is a chart that displays the number “9,999,999” with different radix.
Radix Representation (padded to 25 places)
02 0100110001001011001111111
03 0000000000200211001102100
04 0000000000000212021121333
05 0000000000000010024444444
10 0000000000000000009999999
12 0000000000000000003423053
16 000000000000000000098967f
36 000000000000000000005yc1r
If each number or letter were symbolized by a color and broken up into columns and rows of designated dimensions, pixel image representations could be represented by every number.
For the sake of discovering every picture possible, it’s advantageous to abstract the notion of “every picture possible” down to a restriction of size and color.
DITHERING
Common dithering algorithms. From left to right: Atkinson; Burkes; Floyd–Steinberg; Jarvis, Judice & Ninke; Sierra; Stucki. Davids courtesy of Wikipedia user Gerbrant
Any photo can have a dither algorithm applied to it in order to reduce it to black and white pixels. So by working within a set dimension and using 2 radix numbers (binary) to represent “every picture possible,” imagining the visualization of “every picture possible” becomes graspable. Every picture possible, as seen through a black and white dither, is waiting to be discovered within the existence of numbers themselves.
INTERACTIVE
Upload a photo and see the photo become a number which can be visualized. This should help you imagine how within numbers, every possible image is in existence and just waiting to be discovered.