You are the conductor of a trolley in the complex plane, surrounded on all sides by people, stretching out to infinity, densely covering the entire region | z | ≥ 5 (not fully captured in my MS paint image). The trolley will start at 0 and move iteratively, its next position calculated as f(z) = z\^2 + c, where z is its current position. C is arbitrary. You may set it to any complex number, but cannot change it once the trolley starts moving. However, there's a catch. The people inside the trolley are freezing and rely on the heat generated from the trolley's movement to survive! The faster the trolley moves (on average over the entire trip), the more survive.
What value of c will you choose?
