A fractal is an object that possesses self similarity on different scales, with these scales being related mathematically. E.g., if one chooses a particular region and zooms in 5x, it looks the same. If one zooms in another 5x, it looks the same again, etc. A tiling is a collection of shapes (tiles) that fit together to cover the plane, without overlapping or leaving gaps. A fractal tiling is simply a tiling that possesses fractal character; http://members.cox.net/fractalenc/encyclopedia.html A prototile is a tile to which all other tiles in the tiling are similar; i.e., of the same shape, though not necessarily the same size.



"When life itself seems lunatic, who knows where madness lies? Perhaps to be too practical may be madness. To surrender dreams, this may be madness. To seek treasures where there is only trash...Too much sanity may be madness, and maddest of all is to see life as it is and not as it should be." - Miguel De Cervantes (1547 - 1616), Don Quixote de la Mancha from http://www.quotationspage.com/search.php3?Author=Miguel+de+Cervantes&file=other

"Invention consists in avoiding the constructing of useless contraptions and in constructing the useful combinations which are in infinite minority. To invent is to discern, to choose." - Henri Poincare (1854 - 1912) French mathematician from http://www.quotesandsayings.com/finquoteframes.htm