Tupper's self referential formulae - in MATLAB?

Question

I was trying to plot Tupper's formulae in Matlab. Apparently it seems that since 'k' is such a large value, MATLAB may not accept it.

Any suggestions ?

Answer 1

There is information about arbitrary-length integers in Matlab at http://www.mathworks.com/matlabcentral/newsreader/view_thread/162133; it appears you can use the Symbolic Toolbox to keep the k value and do arithmetic on it in your plot command.

Answer 2

You can use the symbolic toolbox to compute with big integers.

Here is some code I whipped up to plot the Tupper expression, inspired in part by this discussion over at metafilter:

% 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', []);

And the results:

Note: there's not actually anything self-referential about the formula; by choosing a differential value of k, you could make it display any other image of the same size. It would be a lot more exciting if it were an actual quine!