Compute the bitwise XOR of two numbers:

The binary representation of 50 has ones at positions where an odd number of the binary bit representations of 61 and 15 have ones:

Use numbers of any size:

BitXor takes any number of arguments:

Use negative numbers:

Basic symbolic simplifications are done automatically:

Truth table for Xor:

Make a nested pattern:

This structure corresponds to the Sierpiński gasket:

Plot the BitXor of with :

Plot the BitXor of with :

Plot the BitXor of with and :

Generate a Gray code sequence [more info]:

Bitwise version of rule 60 cellular automaton:

-1 corresponds to having all bits on:

Even numbers of identical arguments give 0:

Odd numbers of identical arguments give the argument:

BitXor automatically threads over lists:

BitXor is Orderless:

Plotting BitXor[x,y] in the plane shows a nested pattern of squares:

Plotting in three dimensions reveals a fractal structure:

This structure corresponds to the Sierpiński sponge:

"Munching squares" [more info]: