请用MATLAB实现上述功能
时间: 2023-08-30 22:07:12 浏览: 34
好的,以下是使用MATLAB实现盒计数法计算谢尔宾斯基三角形信息维的代码:
```matlab
% 生成谢尔宾斯基三角形的点集
n = 7;
points = [0, 0; 1, 0; 0.5, 0.5*sqrt(3)];
for i = 1:n
index = randi([1, 3]);
point = points(index, :);
midpoint = (point + points(1 + mod(index, 3), :)) / 2;
points = [points; midpoint];
end
% 计算盒计数
box_sizes = logspace(-3, -1, 100);
box_counts = zeros(size(box_sizes));
for i = 1:length(box_sizes)
box_size = box_sizes(i);
n_x = ceil((max(points(:, 1)) - min(points(:, 1))) / box_size);
n_y = ceil((max(points(:, 2)) - min(points(:, 2))) / box_size);
count = zeros(n_x, n_y);
for j = 1:size(points, 1)
i_x = ceil((points(j, 1) - min(points(:, 1))) / box_size);
i_y = ceil((points(j, 2) - min(points(:, 2))) / box_size);
count(i_x, i_y) = count(i_x, i_y) + 1;
end
n_boxes = sum(count(:) > 0);
box_counts(i) = log(n_boxes) / log(1 / box_size);
end
% 绘制盒计数法图像
loglog(box_sizes, box_counts)
xlabel('log(box size)')
ylabel('log(box count)')
% 计算信息维
p = polyfit(log(box_sizes), box_counts, 1);
disp(['Information dimension: ', num2str(p(1))])
```
运行代码后,会绘制一个盒计数法图像,并输出谢尔宾斯基三角形的信息维。在盒计数法中,`box_sizes`表示盒子的大小,可以通过调整其数值来控制计算盒计数时的盒子大小范围。计算出盒计数后,可以用线性回归来拟合log-log图像,从而得到信息维。