Collage theorem

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In mathematics, the collage theorem characterizes a recurrent functional system whose attractor is close, relative to Hausdorff's metric, to a given set. The IFS is described to consist of contraction images that, as collage or unity when mapping a given set, are arbitrarily close to the given set. This is usually used in fractal compression.

Video Collage theorem

Pernyataan teorema

di mana ${\ displaystyle h (\ cdot, \ cdot)}  ÂÂ$ adalah metrik Hausdorff. Kemudian

${\ displaystyle h (L, A) \ leq {\ frac {\ varepsilon} {1-s}}}  ÂÂ$

dimana A adalah penarik IFS. Secara setara,

${\ displaystyle h (L, A) \ leq (1-s) ^ {- 1} h \ left (L, \ cup _ {n = 1 } ^ {N} w_ {n} (L) \ right) \ quad} Â$ , untuk semua subkumpulan kecil tanpa aturan, L dari ${\ displaystyle \ mathbb {X}} Â Â$ .

Secara informal, Jika $            {\displaystyle         L      }        \{\backslash \; displaystyle\; L\}\;  ÂÂ$ hampir distabilkan oleh IFS, lalu juga hampir menjadi penarik IFS.

Maps Collage theorem

Lihat juga

• Michael Barnsley
• Barnsley pakis

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Referensi

• Barnsley, Michael. (1988). Fraktal Dimana-mana . Academic Press, Inc. ISBN: 0-12-079062-9.

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Tautan eksternal

• Deskripsi teorema kolase dan applet Java interaktif pada cut-the-knot.
• Catatan tentang mendesain IFS untuk mendekati gambar sebenarnya.
• Kertas Eksposisi tentang Fractals and Collage theorem

Source of the article : Wikipedia