In search of self-similar chaotic attractors based on fractal function with variable scaling approximately
Nur Aisyah Abdul Fataf, A. Gowrisankar, Santo Banerjee
Abstract
Abstract This study investigates the reconstruction of self-similar chaotic attractors and virtual functions by mean of fractal interpolation function by choosing vertical scaling parameter as a continuous function on the interval of interpolation. We describe a procedure for the reconstruction of Lorenz attractor and claim that the flexibility on the choice of vertical scaling produce smoother and non-smooth fractal functions which reconstruct the self-affine Lorenz attractor. Apart from approximation and visualization, this paper facilitates fractal function to interact with chaotic systems for proper mild conditions on scaling parameter of fractal functions.
Topics & Concepts
FractalScalingAttractorChaoticStatistical physicsVariable (mathematics)Function (biology)Fractal dimension on networksPhysicsFractal dimensionMathematicsMathematical analysisFractal analysisComputer scienceGeometryArtificial intelligenceBiologyEvolutionary biologyMathematical Dynamics and FractalsChaos control and synchronizationChaos-based Image/Signal Encryption