Differential Equations and Control Processes
(Differencialnie Uravnenia i Protsesy Upravlenia)

Algorithm of Computer Modelling of Julia Set in Case of Parabolic Fixed Point

Author(s):

N. B. Ampilova

Russia, 195251, St.Petersburg, Polytechnicheskaya st., 29,
Saint-Petersburg State Technical University,
Department of Mathematics,

natali@IS1483.spb.edu

E. Petrenko

Russia, 195251, St.Petersburg, Polytechnicheskaya st., 29,
Saint-Petersburg State Technical University,
Department of Mathematics,

natali@IS1483.spb.edu

Abstract:

It is well known that a computer simulation of Julia set for a rational function with a parabolic fixed point deals with problems owing to limited precision of computations. The offered method is based on succesive iterations of small parts of Julia set. The iterations are constructed using the modified method of boundary scanning. The algorithm was implemented for the map f(x)=x²+λx, where λ=exp(2πi/20).

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