The x^x Spindle
The x^x Spindle
It is easy to sketch the graph of for . For , is only defined for rational with odd denominator, unless complex values are allowed. In this case, set =, where log represents the principal branch of the complex logarithm; other branches differ by an integer multiple of and these may be specified using the parameter in the formula. Thus, any value determines a 3D graph where each value determines the point in space . The collection of all of these graphs, or threads, forms the spindle.
y=
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x<0
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x(log(x)+2πk)
2π
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(x,re(),im())
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