Method of detecting, interpreting, recognizing, identifying and comparing n-dimensional shapes, partial shapes, embedded shapes and shape collages using multidimensional attractor tokens

A method for characterizing an m-dimensional shape in an n-dimensional space, comprising the steps of:

• a) configuring a device in at least one of hardware, firmware and software to characterize said m-dimensional shape, said configuring comprising:
• defining labels for a plurality of facial directions of a polytope in said n-dimensional space, said polytope being of k dimensions;
• defining a unit vector for each of said facial directions;
• defining a polytope tiling map for said n-dimensional space;
• and
• defining labels for a plurality of angle types between two or more combinations of said unit vectors;
• b) tiling said m-dimensional shape with said k-dimensional polytope within said n-dimensional space;
• c) mapping a shape into a sequence of angle types;
• d) configuring said device to carry out an attractor process for mapping a source multiset to an attractor space, said attractor process being an iterative process which causes elements in said source multiset to converge on one of at least two different behaviors defined within said attractor space as a result of said iterative process, said configuring step including inputting a characterization of the source multiset to input to said device the number of distinct elements of said source multiset;
• e) using said device, executing said mapping of said sequence of tile addresses to one or more coordinates of said attractor space, each of said coordinates corresponding to a different behavior in the attractor space;
• and
• f) mapping said attractor space coordinates into a target space representation, said target space representation including at least the attractor space coordinates.

A method for characterizing an m-dimensional shape in an n-dimensional space, comprising the steps of:

• a) placing a k-dimensional polytope on a starting point of the m-dimensional shape, said shape being a contour, said polytope having a plurality of faces, each of said faces being associated with an address label;
• b) determining an intersecting face of said polytope intersecting with said shape at an intersecting point;
• c) adding a label corresponding to said intersecting face to a sequence of address labels;
• d) centering said polytope at said intersecting point;
• e) determining an intersecting face of said polytope intersecting with said shape at an intersecting point;
• f) adding a label corresponding to said intersecting face to a sequence of address labels;
• g) repeating steps d) to f) until the entire shape has been addressed, thereby providing a sequence of addresses;
• and
• h) processing said sequence of addresses through an attractor process to obtain a string of one or more tokens, said tokens being indicative of attractor process states resulting from interaction of said attractor process with said sequence.

A method for analyzing an m-dimensional shape in an n-dimensional space, comprising the steps of:

• a) placing a k-dimensional polytope on a starting point of the m-dimensional shape, said shape being a contour, said polytope having a plurality of faces, each of said faces being associated with an address label;
• b) determining an intersecting face of said polytope intersecting with said shape at an intersecting point;
• c) adding a label corresponding to said intersecting face to a sequence of address labels;
• d) centering said polytope at said intersecting point;
• e) determining an intersecting face of said polytope intersecting with said shape at an intersecting point;
• f) adding a label corresponding to said intersecting face to a sequence of address labels;
• g) repeating steps d) to f) until the entire shape has been addressed, thereby providing a sequence of addresses;
• and
• h) processing said sequence of addresses through an attractor process to obtain one or more tokens, said tokens being indicative of attractor process states resulting from interaction of said attractor process with said sequence;
• and
• i) analyzing said tokens to recognize or compare said shape with a set of predetermined shapes.

A method for characterizing an m-dimensional shape in an n-dimensional space, comprising the steps of:

• a) placing a pre-determined point of a k-dimensional polytope on a starting point at an edge of the m-dimensional shape, said polytope having a plurality of faces (k) and a reference point, each of said faces being associated with an address label;
• b) orienting said polytope to place said reference point of said polytope on said edge of said shape
• c) determining an intersecting face of said polytope intersecting with said edge of said shape at an intersecting point;
• d) adding a label corresponding to said intersecting face to a sequence of address labels;
• e) centering said polytope at said intersecting point;
• f) repeating steps b) to e) until the entire shape has been addressed, thereby providing a sequence of addresses;
• and
• g) processing said sequence of addresses through an attractor to obtain a string of one or more tokens, said tokens being indicative of attractor states resulting from said sequence.

A method for analyzing an m-dimensional shape in an n-dimensional space, comprising the steps of:

• a) placing a pre-determined point of a k-dimensional polytope on a starting point at an edge of the m-dimensional shape, said polytope having a plurality of faces (k) and a reference point, each of said faces being associated with an address label;
• b) orienting said polytope to place said reference point of said polytope on said edge of said shape
• c) determining an intersecting face of said polytope intersecting with said edge of said shape at an intersecting point;
• d) adding a label corresponding to said intersecting face to a sequence of address labels;
• e) centering said polytope at said intersecting point;
• f) repeating steps b) to e) until the entire shape has been addressed, thereby providing a sequence of addresses;
• g) processing said sequence of addresses through an attractor to obtain one or more tokens, said tokens being indicative of attractor states resulting from said sequence;
• and
• h) analyzing said tokens to recognize or compare said shape with a set of predetermined shapes.

A device for analyzing an m-dimensional shape in an n-dimensional space, comprising:

• a) means for placing a pre-determined point of a k-dimensional polytope on a starting point at an edge of the m-dimensional shape, said polytope having a plurality of faces (k) and a reference point, each of said faces being associated with an address label;
• b) means for orienting said polytope to place said reference point of said polytope on said edge of said shape
• c) means for determining an intersecting face of said polytope intersecting with said edge of said shape at an intersecting point;
• d) means for adding a label corresponding to said intersecting face to a sequence of address labels;
• e) means for centering said polytope at said intersecting point;
• f) means for repeating steps b) to e) until the entire shape has been addressed, thereby providing a sequence of addresses;
• g) means for processing said sequence of addresses through an attractor to obtain one or more tokens, said tokens being indicative of attractor states resulting from said sequence;
• and
• h) means for analyzing said tokens to recognize or compare said shape with a set of predetermined shapes.

A device for analyzing an m-dimensional shape in an n-dimensional space, comprising a programmed digital computer programmed to perform the steps of:

• a) placing a pre-determined point of a k-dimensional polytope on a starting point at an edge of the m-dimensional shape, said polytope having a plurality of faces (k) and a reference point, each of said faces being associated with an address label;
• b) orienting said polytope to place said reference point of said polytope on said edge of said shape
• c) determining an intersecting face of said polytope intersecting with said edge of said shape at an intersecting point;
• d) adding a label corresponding to said intersecting face to a sequence of address labels;
• e) centering said polytope at said intersecting point;
• f) repeating steps b) to e) until the entire shape has been addressed, thereby providing a sequence of addresses;
• g) processing said sequence of addresses through an attractor to obtain one or more tokens, said tokens being indicative of attractor states resulting from said sequence;
• and
• h) analyzing said tokens to recognize or compare said shape with a set of predetermined shapes.