A quadratic term and a cubic pole
At each step, square the current complex value, then add \(c/z^3\). When \(|z|\) is large, the first term grows roughly like \(|z|^2\), while the reciprocal term fades like \(1/|z|^3\). Near zero the balance flips: the reciprocal term becomes enormous.
The same expression can be written as
$$ f_c(z)=\frac{z^5+c}{z^3}. $$
The map has a pole of order three at \(z=0\), and—when \(c\neq0\)—is a rational map of degree five. The “2–3” names the exponents in the original expression, not the rational-map degree.
In the exact definition, the pole sends zero to infinity on the Riemann sphere. A numerical renderer cannot divide by zero, so FractalPark replaces values extremely close to the origin with a tiny nonzero value and guards the denominator. That is a computational safety rail, not a different definition.
