Apparatus for manifesting latent characteristics existing in sequences of symbols

An apparatus for identifying a repeating sub-sequence within a single linear sequence of alphanumeric data comprising at least a first alphanumeric data representation and a second alphanumeric data representation, comprising:

• means for converting the single linear sequence of the alphanumeric data into at least a first matrix of alphanumeric data, a second matrix of alphanumeric data and a third matrix of alphanumeric data, the first matrix having X columns, the second matrix having Y columns and the third matrix having Z columns, wherein X, Y, Z are integers that are equal or greater than 2 and X, Y and Z are each different integers,
• means for assigning a first color to the first alphanumeric data representation,
• means for assigning a second color to the second alphanumeric data representation, wherein the first color and the second color are different from each other, and
• means for visually displaying the first, second and third matrices of colors in a side-by-side relationship.

An apparatus for expressing at least one characteristic existing in a sequence of symbols I1, I2, . . . Im, wherein m comprises a positive integer, comprising:

• memory arranged and constructed to store the sequence of symbols I1, I2, . . . , Im;
• a processor arranged and constructed to generate parallel sequences A(k) in the form of a matrix X having m matrix elements X(u,v) arranged in n rows and k columns using the sequence of symbols I1, I2, . . . , Im stored in the memory by assigning an element of the sequence of symbols I1, I2, . . . , Im to each matrix element X(u,v), wherein X(u,v)=Ij and one relationship is satisfied from the group consisting of:
• (a) u=┌j÷k┐ and v=j−(┌j÷k┐−1)·k for each value of j satisfying 1≦j≦m,
• (b) u=┌j÷k┐ and v=j−(┌j÷k┐−1)·k for each value of j satisfying 1≦j≦m and ┌j÷k┐ having a value which comprises an odd integer, and
• u=┌j÷k┐ and v=(┌j÷k┐·k)−j+1 for each value of j satisfying 1≦j≦m and ┌j÷k┐ having a value which comprises an even integer,
• (c) u=┌j÷k┐ and v=(┌j÷k┐·k)−j+1 for each value of j satisfying 1≦j≦m, and
• (d) u=┌j÷k┐ and v=(┌j÷k┐·k)−j+1 for each value of j satisfying 1≦j≦m and ┌j÷k┐ having a value which comprises an odd integer, and
• u=┌j÷k┐ and v=j−(┌j÷k┐−1)·k for each value of j satisfying 1≦j≦m and ┌j÷k┐ having a value which comprises an even integer,
• wherein, for each relationship (a)−(d), k comprises an integer satisfying k≧2,
• n=┌m÷k┐,
• ┌m÷k┐ comprises the smallest positive integer having a value that is greater than or equal to the value of m÷k, and
• ┌j÷k┐ comprises the smallest positive integer having a value that is greater than or equal to the value of j÷k;
• the processor being further arranged and constructed to generate at least three matrices selected from matrices X1, X2, . . . , Xp by further parallel-positioning of parallel sequences A(p), A(p+r), A(p+2r), A(p+3r), . . . converted by changing k to p, p+r, p+2r, p+3r, . . . , wherein p comprises an integer satisfying p≦(m÷2), and r comprises an integer;
• and
• visual expression means for visually displaying the at least three matrices using different color hues, color lightness or color saturation, wherein the visual expression means visually displays the at least three matrices in a proximal relationship.

An apparatus for expressing at least one characteristic existing in a sequence of symbols I1,I2, . . . , Im, wherein m comprises a positive integer and the symbols I1,I2, . . . , Im are depicted using a first set of visual representations, comprising:

• means for storing the sequence of symbols I1, I2, . . . , Im;
• means for generating a parallel sequence A(k) in the form of a matrix X having m matrix elements X(u,v) arranged in n rows and k columns using the sequence of symbols I1, I2, . . . , Im stored in the storing means by assigning an element of the sequence of symbols I1, I2, . . . , Im to each matrix element X(u,v), wherein X(u,v) =Ij and one relationship is satisfied from the group consisting of:
• (a) u=┌j÷k┐ and v=j−(┌j÷k┐−1)·k for each value of j satisfying 1≦j≦m,
• (b) u=┌j÷k┐ and v=j−(┌j÷k┐−1)·k for each value of j satisfying 1≦j≦m and ┌j÷k┐ having a value which comprises an odd integer, and
• u=┌j÷k┐ and v=(┌j÷k┐·k)−j+1 for each value of j satisfying 1≦j≦m and ┌j÷k┐ having a value which comprises an even integer,
• (c) u=┌j÷k┐ and v=(┌j÷k┐·k)−j+1 for each value of j satisfying 1≦j≦m, and
• (d) u=┌j÷k┐ and v=(j÷k┐·k)−j+1 for each value of j satisfying 1≦j≦m and ┌j÷k┐ having a value which comprises an odd integer, and
• u=┌j÷k┐ and v=j−(┌÷k┐−1)·k for each value of j satisfying 1≦j≦m and ┌j÷k┐ having a value which comprises an even integer,
• wherein, for each relationship (a)−(d), k comprises an integer satisfying k≧2,
• n=┌m÷k┐,
• ┌m+k┐ comprises the smallest positive integer having a value that is greater than or equal to the value of m÷k and
• ┌j÷k┐ comprises the smallest positive integer having a value that is greater than or equal to the value of j÷k;
• means for generating at least three matrices selected from matrices X1, X2, . . . ,Xp by further parallel-positioning of parallel sequences A(p), A(p+r), A(p+2r), A(p+3r), . . . converted by changing k to p, p+r, p+2r, p+3r, . . . , wherein p comprises an integer satisfying p≦(m÷2), and r comprises an integer;
• means for converting the symbols I1, I2, . . . , Im to a second set of visual representations S1, S2, . . . , Sm, the second set of visual representations differing from the first set of visual representations and comprising a plurality of different colors, color hues, color lightness or color saturation;
• and
• means for visually displaying the at least three matrices X1, X2, . . . , Xp of symbols S1, S2, . . . ,Sm.