Nothing kills a ''quick'' joke like pixelation of older images. Sigh.
Originally, I was just going to substitute the other AnthroNumeric(tm) characters, but then I decided I should match the colors and faces. Ooooh, bad decision.

If you take numbers ending in 1 to 9 and raise them to the second power, they will end in 1, 4, 9, 6, 5, 6, 9, 4, 1.
If you raise them to the third power, they will end in 1, 8, 7, 4, 5, 6, 3, 2, 9.
If you raise them to the fourth power, they will end in 1, 6, 1, 6, 5, 6, 1, 6, 1.
And, finally, if you raise them to the fifth power, you return to 1, 2, 3, 4, 5, 6, 7, 8, 9, and the cycle will start over again.

The interesting things here:
In 1, 5, 6, and 0, if included, never change.
Row 2 is symmetrical (if you leave out 0). Also, no perfect square ends in 2, 3, 7 or 8.
Row 3 uses all nine numbers from 1 to 9.
Row 4 is also symmetrical and only contains 3 numbers. (That pesky 5!)