Github has these default avatars they call identicons that are 5x5 grids with a single color. They are generated using a hashing function and a username as a seed. Despite the grid being 5x5, they are always symmetrical, so the grid is actually 3x5 with column 4 being the same as column 2 and column 5 being the same as column 1.

A 3x5 grid has only 15 squares, and a square is either on or off. It dawned on me one day that the total number of permutations isn't actually *that* large. 2^15 = 32,768.

As a hobbyist generative artist, this screamed small multiples to me.

## Generating an avatar

An avatar can be thought of as a 15 digit binary number, where each bit represents one of the fifteen squares in the 3x5 grid. Then the first two columns are reflected across the middle column.

```
avatar = 100 010 001 010 001
1 0 0 0 1
0 1 0 1 0
0 0 1 0 0
0 1 0 1 0
1 0 0 0 1
```

Using Processing (with Python instead of Java), this binary avatar can be turned into lovely rectangles using the following set of loops and bitwise operations:

```
def avatar(seed, avatarSize = 50):
paddingSize = floor(avatarSize * 0.05)
tileSize = ceil(avatarSize * 0.9 / 5)
noStroke()
# Set a gray background
fill(0, 0, 245)
rect(0, 0, avatarSize, avatarSize, paddingSize, paddingSize, paddingSize, paddingSize)
# Choose a randomish color for the avatar
fill(random(255), random(25, 75), random(175, 225))
pushMatrix()
translate(paddingSize, paddingSize)
for i in range(5):
for j in range(3):
# If the bit in this square's position in the seed int is flipped, then draw a square
if seed & (1 << (i * 3 + j)):
rect(tileSize * j, tileSize * i, tileSize, tileSize)
# For the first two columns, also draw a square in the reflected column
if j != 2:
rect(tileSize * (4 - j), tileSize * i, tileSize, tileSize)
popMatrix()
```

## Generating all the avatars

Since generating an avatar has been reduced to a binary seed, generating all the avatars is as simple as iterating over all the binary values between `000 000 000 000 000`

and `111 111 111 111 111`

. Since binary is just a base 2 number, we can instead think of these seeds as base 10 numbers. This makes the range `0..32768`

.

```
for i in range(32768):
avatar(i)
```

This will work for generating every single avatar, but I also wanted to see everything at once. I wanted the small multiples. Withouth thinking too hard, I just found a couple reasonable factors of 2^15 to make a nice arrangement. 2^7 × 2^8 = 2^15. Good enough!

```
pushMatrix()
translate(50, 50)
for x in range(128):
for y in range(256):
pushMatrix()
translate(23 * x, 23 * y)
avatar(y * 128 + x, 22)
popMatrix()
popMatrix()
save('tiles-full.png')
```

## Technology Used

- Processing
- Python