Conservative Byte Drift Machine

Call a machine that returns bytes for translated bytes while keeping the number of 1-bits constant a "conservative byte drift machine". An initial 3D array of bits is translated according to a drift vector that specifies shifts along the three axes. The array is then partitioned into cubes of size 2.
Each octet of bits is transduced into the same number of bits at new octet positions according to a rule given by 256 base-256 digits. These 256 digits of the rule are represented by a rule icon which shows each base-256 digit by the hue of a pixel.
Click the rule icon to obtain a new rule number.



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In order for a rule to act conservatively at each step, the number of 1-bits in each rule digit must be equal to the number of 1-digits in its Wolfram rule-order digit-position. Among all 256256 rules which return bytes for bytes, the natural logarithm of the number of distinct conservative rules is 968.108573542480638.
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