Title: Perturbation for Julia Post by: Kalles Fraktaler on October 31, 2014, 12:41:19 PM 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........... :hurt: Title: Re: Perturbation for Julia Post by: Kalles Fraktaler on April 23, 2015, 08:53:57 PM 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 Dn = Yn - Xn not applicable for Julia? |