Parabolic orbits, critical orbit, attracting petals and upper main chessboard box for f(z) = z^2 +0.25. Tt is a part of dynamical plane of discete dynamical system based on the complex quadratic poynomial fc(z)=z2+c{\displaystyle f_{c}(z)=z^{2}+c}. Points of critical orbit ( including crirital point and parabolic attractor) are on the level curves like notes on the musical staff. Algorithm : "An often used and very useful technique of visualization of ramified covers (and partial cover structures that are not too messy) consists in cutting the range in domains, often simply connected, along lines joining singular values, and taking the pre-image of these pieces, which gives a new set of pieces. The way they connect together and the way they map to the range give information about the structure." Arnaud ChéritatNear Parabolic Renormalization for Unicritical Holomorphic Maps by Arnaud Chéritat[1]
Own work
Adam majewski