Rule 90

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:

规则 90 是一个具有有趣属性的一维元胞自动机。

规则很简单。有一个一维单元格数组（打开或关闭）。在每个时间步中，每个单元的下一个状态是单元的两个当前邻居的异或。下表是表达此规则的更详细的方式，其中单元格的下一个状态是其自身及其两个相邻单元的函数：

题目网站

module top_module(
    input clk,
    input load,
    input [511:0] data,
    output [511:0] q ); 
    integer i;
    always@(posedge clk)begin
        if(load)begin
            q<=data;
        end
        else begin
            q<={1'b0,q[511:1]}^{q[510:0],1'b0};
        end
    end
endmodule

这个写法画一个图方便理解，是从整体出发的写法：

从这个图可以看出q<={1'b0,q[511:1]}^{q[510:0],1'b0};中第一位0^{b就是原数列a的左右两位的异或，第二位a}c就是原数列b的左右两位的异或……依此类推可得。

下面提供另一种写法：

module top_module(
    input clk,
    input load,
    input [511:0] data,
    output [511:0] q ); 
	always @(posedge clk ) begin
        if(load)begin
            q <= data; 
        end
        else begin
            q <= (q<<1)^(q>>1);
        end
    end
endmodule

这个写法用q <= (q<<1)^(q>>1);，写的更直观。