Perturbation of Mandelbrot set fractal

fractals

Solution 1:

Your computation is correct:

$\Delta_2 = (4X_1 X_0 + 2 X_1 + 1) \delta + (2X_1 + (2X_0 + 1)^2)\delta^2 + (4X_0+2)\delta^3+\delta^4$

Their computation for the induction is correct:

$ A_{n+1} = 2 X_n A_n + 1 \\ B_{n+1} = 2 X_n B_n + A_n^2 \\ C_{n+1} = 2 X_n C_n + 2 A_n B_n $

Initialise $A_0 = 1, B_0 = 0, C_0 = 0$ and use their computation for the induction.

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