The model shown in the figure converts all numbers that have k digits in the binary system to Gray code without any calculation, but I have no proof that guarantees this claim.

Here is some information on how to use it.

Conversion model of all integers that have k digits in the binary system in Gray code.

Rules

You will need k columns of numbers. The numbers to be encoded are arranged in the last column.

The conversion is done gradually by transferring groups of numbers to the adjacent columns in the way the arrows show. There are two types of paired arrows, parallel (=) and intersecting (×). Symbolically, the (=) and (×) are considered inverse of each other.

Each column with arrows is formed by an exact copy of the previous column and by a copy of the previous column that has inverted pairs of arrows, which is placed below the exact copy.

Observation

If we set "=" = 0 and "×" = 1, then the successive columns containing arrows form the Thue Morse sequence which essentially forms the rules for converting integers to Gray code.