Basically I started by finding algebraic curves that had shapes I liked. So that means polynomials in x and y whose zero sets/varieties in the plane were cool shapes. I would sometimes take a couple polynomials in order to have multiple interesting shapes at once. Then I would write those polynomials down in terms of the real and imaginary parts of a complex number z and add the sum of the inverses of them to the equation being used to make a Julia set. I tried some variations but that was the basic idea. The reason it worked was that anytime the software examined points near the zero sets of the polynomials, the function generating the julia set would send those points towards infinity so they would all end up colored the same way. This method is not at all true to what Julia sets are, in fact it is a pretty awful thing. But some cool images came out of it.
A mistake from early on
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