Given two positive numbers, x and y, it is not always easy to predict which is larger, x^y or y^x. We see that 2^3 < 3^2, 2^4 = 4^2, and 3^4 > 4^3. This problem caused me to want a contour map of z = x^y - y^x. In the process of writing and checking out a program to generate this map, I became more interested in the beauty of the pattern being generated than in the original problem. The pseudo code for the program is: BEGIN Draw box around edge of screen FOR all y pixels YG in box from top DO BEGIN Y:= (MaxYPix - YG) * Scale; FOR all x pixels XG in box from left DO BEGIN X:= XG * Scale; Z:= Y^X - X^Y; IF Z <= -10.0 THEN Z:= -Z; { For large |Z|, use } IF Z >= 10.0 THEN Z:= Log(Z); { log base 10 scale } IF Z < 0 THEN Z:= 0.5 - Z; { Plot < 0 opposite of > 0 } ZG:= TRUNC(2.0 * Z) MOD 2; { Contour line every Z = 1/2 n } IF ZG = 1 THEN plot a dot at (XG, YG); END; END; END.

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