Rule90

From HDLBits

Rule 90 is a one-dimensional cellular automaton with interesting properties.

The rules are simple. There is a one-dimensional array of cells (on or off). At each time step, the next state of each cell is the XOR of the cell's two current neighbours. A more verbose way of expressing this rule is the following table, where a cell's next state is a function of itself and its two neighbours:

LeftCenterRightCenter's next state
1110
1101
1010
1001
0111
0100
0011
0000

(The name "Rule 90" comes from reading the "next state" column: 01011010 is decimal 90.)


In this circuit, create a 512-cell system (q[511:0]), and advance by one time step each clock cycle. The load input indicates the state of the system should be loaded with data[511:0]. Assume the boundaries (q[-1] and q[512]) are both zero (off).

Module Declaration

module top_module(
    input clk,
    input load,
    input [511:0] data,
    output [511:0] q ); 

For an initial state of q[511:0] = 1, the first few iterations are:

       1
      10
     101
    1000
   10100
  100010
 1010101
10000000

This forms half of a Sierpiński triangle.

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