FRACTAL INTERPOLATION FUNCTIONS ON AFFINE FRACTAL INTERPOLATION CURVES

Songil Ri, Songmin Nam and Hyonchol Kim
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Songil Ri: Faculty of Mathematics, University of Science, Pyongyang, DPR Korea
Songmin Nam: Faculty of Management, Pyongyang University of Transport, Pyongyang, DPR Korea
Hyonchol Kim: Faculty of Mathematics, Kim Il Sung University, Pyongyang, DPR Korea

FRACTALS (fractals), 2021, vol. 29, issue 02, 1-16

Abstract: In this paper, we give fractal interpolation functions generated on some special affine fractal interpolation curve by harmonic functions of fractal analysis. In the case of Koch Curve, same statement is regarded as a corollary, that is, we show that it is possible to ensure that graphs of fractal interpolation functions on the Koch Curve are attractors of iterated function systems.In the case of fractal interpolation functions generated on general affine fractal interpolation curves by harmonic functions of fractal analysis, all the discussions are similar to those performed in some special affine fractal interpolation curve if their harmonic structures are given.

Keywords: Iterated Function System (IFS); Fractal Interpolation Function (FIF); Koch Curve (KC); Harmonic Function; Hölder Continuity (search for similar items in EconPapers)
Date: 2021
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DOI: 10.1142/S0218348X21500468

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