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A regular two-dimensional arrangement of squares separated by vertical and horizontal "canals." Looking at the grid produces the illusion of gray spots in the white area ...

The bound for the number of colors which are sufficient for map coloring on a surface of genus g, gamma(g)=|_1/2(7+sqrt(48g+1))_| is the best possible, where |_x_| is the ...

Flower graphs are a name given in this work to the generalization of the flower snarks J_n for positive n=5, 7, 9, ... to all integer n>=5. They are illustrated above for n=5 ...

An optical illusion named after British psychologist James Fraser, who first studied the illusion in 1908 (Fraser 1908). The illusion is also known as the false spiral, or by ...

A class of illusion in which an object which is physically unrealizable is apparently depicted. More than 100 papers have been written about impossible figures (Kulpa 1987), ...

In the above illustration, black dots appear to form and vanish at the intersections of the gray horizontal and vertical lines. When focusing attention on a single white dot, ...

A plane image or pair of two-dimensional images that, when appropriately viewed using both eyes, produces an image which appears to be three-dimensional. By taking a pair of ...

An ambiguous figure in which the brain switches between seeing a rabbit and a duck. The duck-rabbit was "originally noted" by American psychologist Joseph Jastrow (Jastrow ...

The number of colors sufficient for map coloring on a surface of genus g is given by the Heawood conjecture, chi(g)=|_1/2(7+sqrt(48g+1))_|, where |_x_| is the floor function. ...

The vectors +/-a_1, ..., +/-a_n in a three-space form a normalized eutactic star iff Tx=x for all x in the three-space.