Tupper independent reference formulas - in MATLAB?

Question

I tried to build Tupper Formulas in Matlab. It seems that, since "k" is such a large value, MATLAB may not accept it.

Any suggestions?

Answer 1

You can use the symbolic toolbar to calculate with large integers.

Here is some code that I whipped to build a Tupper expression, based in part on this discussion in 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 native double precision tupper = double(tupper); % display it! image(fliplr((1-tupper)*255)); colormap gray axis equal title('Tupper' (not-so-)self-referential formula!'); set(gca, 'XTick', [], 'YTick', []); 

And the results:

Note: in fact, there is nothing self-referential regarding the formula; by choosing a differential value of k , you can display any other image of the same size. It would be much more interesting if it was a real game!

Answer 2

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