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No. 887: Complex Square Root of Minus Garfield

Complex Square Root of Minus Garfield

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Strip by: David Morgan-Mar

Jon: Hi, there... I'm Jon Arbuckle. I'm a cartoonist, and this is my cat, Garfield.
Garfield: Hi, there. I'm Garfield. I'm a cat, and this is my cartoonist, Jon.
Jon: Our only thought is to entertain you.
Garfield: Feed me.

The author writes:

Seeing Neil's submissions in which he applied the complex square root function to the hue of strips (#849, #885), I realised that at my work we have custom image processing software designed to handle complex-valued pixels. (We use it for 2-dimensional Fourier transforms, which require complex numbers to be stored at each pixel location.) So I imported a selected Garfield strip, copied the red and green channels into the real and imaginary components, took the negative of the image ("minus"), and then applied a complex square root. Copying the resulting real and imaginary components back into red and green channels gave this result.

Unfortunately I couldn't think of any good way to also include the blue channel information in this operation, so it is unchanged. I considered using a quaternion representation (which our software can also do), mapping blue into the j channel, and leaving the k channel empty, then applying a square root, but I didn't see an easy way of implementing the quaternion square root operation in the 2 minutes I spent making this strip. Consider this a challenge to any maths nerds out there...

Original strip: 1978-06-19.