Tupper的自我指称公式 - 在MATLAB中？

Question

我试图在Matlab中绘制Tupper的公式.显然,似乎因为'k'是如此大的值,MATLAB可能不会接受它.

有什么建议 ？

Answer 1

您可以使用符号工具箱来计算大整数.

下面是一些我编写的用于绘制Tupper表达式的代码,部分受到metafilter讨论的启发:

% use the symbolic toolbox to represent the big integer k
k =  sym(['960939379918958884971672962127852754715004339660129306651505519271702802395266424689642842174350' ...
    '718121267153782770623355993237280874144307891325963941337723487857735749823926629715517173716995' ...
    '165232890538221612403238855866184013235585136048828693337902491454229288667081096184496091705183' ...
    '454067827731551705405381627380967602565625016981482083418783163849115590225610003652351370343874' ...
    '461848378737238198224849863465033159410054974700593138339226497249461751545728366702369745461014' ...
    '655997933798537483143786841806593422227898388722980000748404719']);

[x,y] = meshgrid(0:1:106, 0:1:16);

% evaluate the tupper formula
tupper = rem(floor(floor((y+k)/17) .* 2.^(-17*x - rem((y+k), 17))), 2);

% convert from symbolic to Matlab's native double precision
tupper = double(tupper);

% display it!
image(fliplr((1-tupper)*255));
colormap gray
axis equal

title('Tupper''s (not-so-)self-referential formula!');
set(gca, 'XTick', [], 'YTick', []);

结果如下:

注意:关于公式实际上没有任何自我指涉; 通过选择差值k,可以使其显示相同大小的任何其他图像.如果它是一个真正的quine会更令人兴奋!