About Shape of Julia Sets Analogous on Double Numbers Plane
2009jbo | Pavlov D.G., Panchelyuga M.S., Panchelyuga V.A.  // Research Institute of Hypercomplex Systems in Geometry and Physics, Friazino, Russia, Institute of Theoretical and Experimental Biophysics of RAS, Pushchino, Russia, panvic333@yahoo.com

Double-numbers analogous of Julia sets pre-fractals in the case of iteration of $z_{n+1} \to z_{n}^{2} +c,$ for $c\neq0$ are constructed. Numerical algorithm, which allows correct visualization of the Julia set pre-fractals is described and limits of it applicability in the case of $c=0$ are illustrated. Analytical methods, which allow studying of the Julia sets shapes are described and application of the methods to pre-fractals of low orders is demonstrated.

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