Functions with Multiple Periods
Functions with multiple variables can have multiple periods.
Out[1]= | ![](HTMLImages.en/functions-with-multiple-periods/O_23.png) |
Tesselating rectangles split the plane into regions where the function repeats.
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Out[2]= | ![](HTMLImages.en/functions-with-multiple-periods/O_24.png) |
A function of a single complex variable can have two periods, in two different complex directions.
Out[3]= | ![](HTMLImages.en/functions-with-multiple-periods/O_25.png) |
Out[4]= | ![](HTMLImages.en/functions-with-multiple-periods/O_26.png) |
Adding either of these periods to the input variable will leave the function unchanged.
Out[5]= | ![](HTMLImages.en/functions-with-multiple-periods/O_27.png) |
However, in this example the two complex directions are not perpendicular.
Out[6]= | ![](HTMLImages.en/functions-with-multiple-periods/O_28.png) |
This means that the repeating blocks in the complex plane are parallelograms rather than rectangles.
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Out[7]= | ![](HTMLImages.en/functions-with-multiple-periods/O_29.png) |