Any hexagram may be transformed into any other by changing certain lines. If more than one line needs to be changed, the original hexagram is transformed into a number of intermediates along the way. The conventional transitional hexagrams are one path from the base to the transformed hexagram, made by transforming the moving lines from bottom to top. But the lines may actually be changed in any order; and the more lines that need to be changed, the more pathways there are to take. (It is actually the factorial, or n!, of the number of changed lines, which in the case of six lines is 720.) Larry Schoenholtz advocated making use of such creative mutation in New Directions in the I Ching.
Choose two hexagrams below, and the script will generate all possible single-line transition pathways between them, and list all of the transitional hexagrams. (May run slow in older browsers, especially Internet Explorer.)