A machine that returns four bits for translated hexadecimals while keeping the number of 1-bits constant is called a conservative hex drift machine.
An initial 2D array of bits is translated according to a drift vector that specifies shifts along the two axes. The array is then partitioned into square arrays of size 2. Without drift local quartets evolve in isolation.
Each quartet of bits is transduced into the same number of bits at new quartet positions according to a rule given by 16 base-16 digits. These 16 digits of the rule are represented by a rule icon that represents each base-16 digit by the hue of a pixel.
A byte machine rule is conservative if the number of 1-bits in each rule digit is equal to the number of 1-digits in its Wolfram rule-order digit-position. Choose permutations of conservative replacement rules which mix all possible loops or select a list of rules from the wider ranges of arbitrary conservative replacements. Try to direct the drift vector while compensating its visual effect.
The fourteen rule icons between the controls and the main image are ordered and divided according to their digit-sums. This subdivision of the rule icons corresponds to the effects of the controls which select from loop rules or ordinary conservative rules. The selected 1-loop rule specifies what permutation of all the 24 permutations of the four digits in the binary number 1000 defines the particular rules for each hex containing just one 1-bit. Similarly an 11-loop rule specifies one permutation of all the permutations of the bits in the binary number 1100, etc. The non-loop rules permit arbitrary selections of four right-hand-side hex configurations from the 24 permutations of the digits in binary number 1000, thus allowing selective rules that, for instance, take all hex values with only one 1-bit to only one particular one 1-bit hex configuration.