| Jonathan Bowers' Array Notation |
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RULES # For one- and two-element arrays, just add the elements. = a and [a,b = a+b # If rule 1 does not apply, and if there are any trailing 1's, remove them: = [a,b ; = [a,b,c , etc. # If neither previous rule applies, and the 2nd entry is a 1, remove all but the first element: = [a = a. # If none of the previous rules applies, and the 3rd entry is a 1: Define the variables a,b,S,d and R so that the array is where a,b are the first two elements, [S,1 is the string of 1 or more 1's; d is the first element bigger than 1 and is the remaining part of the array. Replace the array with [a,a,S',[a,b-1,S,1,d,R ,d-1,R] where is a string of a's of equal length as string [S . # If none of the previous rules applies, replace the second element: becomes [a,[a,b-1,c,R ,c-1,R]. EXAMPLES {Link without Title} = [2,[2,1,2,2 ,1,2] (by rule 5) {Link without Title} = 2 (by rule 3) so we have {Link without Title} = [2,2,[2,1,1,2 ,1] (by rule 4) {Link without Title} = 2 (by rule 3) so we have {Link without Title} = [2,2,2 (by rule 2) = [2,[2,1,2 ,1] (by rule 5) {Link without Title} = 2 (by rule 3) so we have {Link without Title} = [2,2 (by rule 2) {Link without Title} = 2+2 = 4 (by rule 1) {Link without Title} = [3,[3,1,2,2 ,1,2] (by rule 5) = {Link without Title} ,1] (by rule 4) = {Link without Title} ,1],1] (by rule 4 again) = [3,3, 3,3,3 (by rule 2) = {Link without Title} ,2]] (by rule 5) = {Link without Title} ,2],2]] (by rule 5) = {Link without Title} ,1],2]] (by rule 5) = {Link without Title} ,1],1],2]] (by rule 5) = 3,3 ,2 ] (by rules 2 and 3) = {Link without Title} ,2]] (by rule 1) = [3,3, 3,9,2 (by rule 1) ... (about 8 repeats of rules 5 and 1 to turn {Link without Title} into 27) SEE ALSO LINKS |
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