The Bresenham line algorithm is an algorithm which determines which points in an n-dimensional raster should be plotted in order to form a close approximation to a straight line between two given points. It is commonly used to draw lines on a computer screen, as it uses only integer addition, subtraction and bit shifting, all of which are very cheap operations in standard computer architectures. It is one of the earliest algorithms developed in the field of computer graphics. A minor extension to the original algorithm also deals with drawing circles.
While algorithms such as Wu's algorith...
Pretty cool; EquationalLogic`FindCounterexample is still pretty mysterious (at least to me), but I managed to get it to do something more interesting than spit back numbers.
In[1]:= EquationalLogic`FindCounterexample[f[a, i] == a, f[a, a] == a]
Out[1]:= {{f -> ({{1, 2}, {1, 1}}[[##1]] &...
For solving ODEs like yours for a variable number of functions, you could do something like:
dims = 3;
k = RandomInteger[{-2, 2}, {dims, dims}];
DSolve[Table[
D[f[i, x], x] == Table[f[j, x], {j, dims}].k[[i]] &&
(D[f[i, x], x] /. x ->...
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