我们知道,利用矩阵可以求解斐波那契类型的递推数列的通项公式.事实上很多递推问题都可以利用矩阵解决.我们来看下面这样一个有趣的数学游戏:一个正方形,画出它的中点正方形;再画出新正方形的中点正方形,依此类推,会生成一个漂亮的图案.如果在原正方形的四个顶点处随意各写一个自然数,将相邻顶点处的自然数相减(用较大的数减较小的数,若两数相等,则差为0,称这种运算为相邻做差运算),计算结果写在每 We know that using matrices solves the general formula for Fibonacci recursion sequences. In fact, many recursion problems can be solved using matrices. Let’s look at an interesting math game like this: a square, draw it Of the midpoint of the square; then draw a new square of the midpoint of the square, and so on, will generate a beautiful pattern.If the original square at the four vertices at random write a natural number, subtract the natural number of adjacent vertices ( With a larger number minus the smaller number, if the two equal, then the difference is 0, saying that this operation is adjacent to do bad operation), the calculation results written in each