PERAN FAKTOR PENYEKALA PADA KONSTRUKSI INTERPOLASI FRAKTAL
DOI:
10.29303/jpm.v7i2.100Published:
2012-09-01Issue:
Vol. 7 No. 2 (2012): SeptemberArticles
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Abstract
Abstrak: Telah diketahui bahwa suatu fungsi fraktal ÃÂ yang menginterpolasi data ÃÂ sedemikian hingga ÃÂ untukÃÂ ÃÂ dapat dikonstruksi dari suatu Sistem Fungsi Iterasi (SFI) berdasarkan teorema titik tetap pada pemetaan kontraktif. Dengan mengambil suatu bentuk pemetaan Affine, yang merupakan salah satu bentuk pemetaan kontraktif untuk SFI, dapat dibuktikan eksistensi atraktor SFI dimaksud yang tidak lain merupakan interpolan fraktal dari data terkait. Faktor penyekala ÃÂ yang termuat di dalam pemetaan affine memegang peran sebagai syarat perlu eksistensi dan ketunggalan fungsi interpolasi fraktal suatu data. Syarat perlu tersebut berlaku pada batasan nilai .
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Kata kunci : interpolan fraktal, SFI, teorema titik tetap, pemetaan affine, faktor penyekala.
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Abstract: It is known that a fractal functions àthat interpolated the data àsuch that , àcan be constructed from an Iterated Function System (IFS) based on The Fixed Point Theorem on contractive mappings. By taking a certain Affine Mapping, which is a form of contractive mapping on IFS, the existence of IFSââ¬â¢ attractor can be proven as the àfractal interpolan of related data. The vertical scaling factor àcontained in the affine mapping role as a necessary condition of existence and uniqueness of a fractal interpolation function data. The necessary condition ofààis on the interval .
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Keywords : ÃÂ ÃÂ fractal interpolan, IFS, The Fixed Point Theorem, Affine Mapping,ÃÂ vertical scaling factor)License
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