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Algebraic Numbers of Degree 2

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The red points represent a specific subset of the Algebraic numbers. A number is algebraic if it can be a solution to a non-zero polynomial with only whole number coefficients, this is almost all of the numbers most people are familiar with: whole numbers, fractions, the square root of -1, and some irrationals like the square roots of primes. A number that isn't algebraic is transcendental. Despite pi and e being the only famous examples, almost all numbers are actually transcendental. The specific subset of the Algebraics used here is one of the simplest; they are the solutions to quadratics with coefficients no greater in magnitude than 100.

The frame extends six fifths into the complex plane in the positive and negative, real and imaginary directions. The line of real numbers runs horizontally through the image, and the points on that line which are isolated are whole numbers. Particularly clear is the unit circle; the set of points of distance 1 from the origin.
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© 2013 - 2021 Fauxtographique
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hunterfly's avatar
how did you make this? matlab? :O
Fauxtographique's avatar
I wrote a Python script to generate it, utilising Python Imaging Library.