Perturbation for Julia

[Kalles Fraktaler]

I wanted to try to render a Julia fractal with Perturbation, but I failed.

This is how I applied the Julia formula to master K.I.Martin's functions:
X[n+1] = X[n]^2 + C
Y[n+1] = X[n+1] + D[n+1]
D[n+1] = Y[n+1] - X[n+1]
D[n+1] = (Y[n]^2 + C) - (X[n]^2 + C)
D[n+1] = ((X[n] + D[n])^2 + C) - (X[n]^2 + C)
D[n+1] = X[n]^2 + 2*X[n]*D[n] + D[n]^2 + C - X[n]^2 - C
D[n+1] = 2*X[n]*D[n] + D[n]^2 (1)

A nice thing with Julia is that the constant C, that needs to be full precision, is eliminated.
So... now it is time for extracting the complex variables

(dr+di) = 2*(xr+xi)*(dr+di) + (dr+di)
(dr+di) = 2*(xr*dr + xr*di + xi*dr - xi*di) + dr*dr + 2*dr*di - di*di
dr = 2*(xr*dr - xi*di) + dr*dr - di*di
di = 2*(xr*di + xi*dr) + 2*dr*di

And............................. it doesn't work........... 

[Kalles Fraktaler]

Have anyone had a look on this?

Is it because the the X and the Y is not starting with the same value for Julia, that makes K.I.Martin's equation
D
_n = Y_n - X_n not applicable for Julia?