[{"@context":"http:\/\/schema.org\/","@type":"BlogPosting","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/22441#BlogPosting","mainEntityOfPage":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/22441","headline":"\u7e70\u308a\u8fd4\u3057\u6a5f\u80fd\u30b7\u30b9\u30c6\u30e0-Wikipedia","name":"\u7e70\u308a\u8fd4\u3057\u6a5f\u80fd\u30b7\u30b9\u30c6\u30e0-Wikipedia","description":"before-content-x4 a \u7e70\u308a\u8fd4\u3057\u6a5f\u80fd\u30b7\u30b9\u30c6\u30e0 \uff08 ifs \uff09\u305f\u304f\u3055\u3093\u3067\u3059 f {displaystyle {mathcal {f}}} after-content-x4 \u540c\u3058\u7a7a\u9593\u3067\u3042\u308b\u95a2\u6570\u304b\u3089 m {displaystyle m} \u5b9a\u7fa9\u3068\u5024\u306e\u7bc4\u56f2\u3068\u3057\u3066\u3001\u30ea\u30f3\u30af\u3067\u5b8c\u4e86\u3057\u307e\u3059\u3002\u305d\u308c\u3067 after-content-x4 F\u2218 F\u2282 F{displaystyle","datePublished":"2023-03-05","dateModified":"2023-03-05","author":{"@type":"Person","@id":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/author\/lordneo#Person","name":"lordneo","url":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/author\/lordneo","image":{"@type":"ImageObject","@id":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","url":"https:\/\/secure.gravatar.com\/avatar\/44a4cee54c4c053e967fe3e7d054edd4?s=96&d=mm&r=g","height":96,"width":96}},"publisher":{"@type":"Organization","name":"Enzyklop\u00e4die","logo":{"@type":"ImageObject","@id":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","url":"https:\/\/wiki.edu.vn\/wiki4\/wp-content\/uploads\/2023\/08\/download.jpg","width":600,"height":60}},"image":{"@type":"ImageObject","@id":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/205d4b91000d9dcf1a5bbabdfa6a8395fa60b676","url":"https:\/\/wikimedia.org\/api\/rest_v1\/media\/math\/render\/svg\/205d4b91000d9dcf1a5bbabdfa6a8395fa60b676","height":"","width":""},"url":"https:\/\/wiki.edu.vn\/all2jp\/wiki10\/archives\/22441","wordCount":9489,"articleBody":"     (adsbygoogle = window.adsbygoogle || []).push({});before-content-x4a \u7e70\u308a\u8fd4\u3057\u6a5f\u80fd\u30b7\u30b9\u30c6\u30e0 \uff08 ifs \uff09\u305f\u304f\u3055\u3093\u3067\u3059 f {displaystyle {mathcal {f}}}        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4\u540c\u3058\u7a7a\u9593\u3067\u3042\u308b\u95a2\u6570\u304b\u3089 m {displaystyle m} \u5b9a\u7fa9\u3068\u5024\u306e\u7bc4\u56f2\u3068\u3057\u3066\u3001\u30ea\u30f3\u30af\u3067\u5b8c\u4e86\u3057\u307e\u3059\u3002\u305d\u308c\u3067        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4F\u2218 F\u2282 F{displaystyle {mathcal {f}} circ {mathcal {f}} subset {mathcal {f}};} d\u3002 h\u3002 \u2200 f \u3001 g \u2208 F\uff1a f \u2218 g \u2208 F\u3002 {displaytyle; formall f\u3001gi {mathcal {f}}\uff1a; fcirc gi {matcal {f}} \u901a\u5e38\u3001\u6a5f\u80fd\u30b7\u30b9\u30c6\u30e0\u306f\u30d5\u30e9\u30af\u30bf\u30eb\u3092\u8a2d\u8a08\u3059\u308b\u306e\u306b\u5f79\u7acb\u3061\u307e\u3059\u3002 ifs -fractal \u6307\u5b9a\u3055\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u306e\u30af\u30e9\u30b9\u306e\u30d5\u30e9\u30af\u30bf\u30eb\u306e\u6709\u540d\u306a\u4ee3\u8868\u8005\u306f\u3001\u30b7\u30a8\u30eb\u30d4\u30f3\u30b9\u30ad\u30fc\u306e\u4e09\u89d2\u5f62\u3068\u8abf\u7406\u66f2\u7dda\u3001\u304a\u3088\u3073\u30ea\u30f3\u30c7\u30f3\u30de\u30a4\u30e4\u30fc\u30b7\u30b9\u30c6\u30e0\u306e\u9650\u754c\u91cf\u3067\u3059\u3002 \u3053\u306e\u30bf\u30a4\u30d7\u306e\u30d5\u30e9\u30af\u30bf\u30eb\u5efa\u8a2d\u306f\u30011981\u5e74\u306b\u30b8\u30e7\u30f3\u30cf\u30c3\u30c1\u30f3\u30bd\u30f3\u306b\u3088\u3063\u3066\u767a\u660e\u3055\u308c\u307e\u3057\u305f [\u521d\u3081] \u305d\u3057\u3066\u5f8c\u306b\u5f7c\u306e\u672c\u3067\u30de\u30a4\u30b1\u30eb\u30fbF\u30fb\u30d0\u30fc\u30f3\u30ba\u30ea\u30fc\u306b\u3088\u3063\u3066 \u3069\u3053\u3067\u3082\u30d5\u30e9\u30af\u30bf\u30eb [2] \u5927\u8846\u5316\u3002 [3] \u30d0\u30fc\u30f3\u30ba\u30ea\u30fc\u3082\u305d\u308c\u3092\u4e0e\u3048\u307e\u3057\u305f \u30b3\u30e9\u30fc\u30b8\u30e5\u30bb\u30c3\u30c8 \u30d5\u30e9\u30af\u30bf\u30eb\u5727\u7e2e\u306b\u57fa\u3065\u3044\u3066\u5f62\u6210\u3055\u308c\u307e\u3059\u3002\u305f\u3060\u3057\u3001\u30c7\u30fc\u30bf\u69cb\u9020\u3092\u4f7f\u7528\u3057\u3066\u753b\u50cf\u3092\u52b9\u7387\u7684\u306b\u30b3\u30fc\u30c7\u30a3\u30f3\u30b0\u3059\u308b\u3053\u306e\u65b9\u6cd5\u306f\u3001\u9069\u5207\u306b\u512a\u5148\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u305a\u3001\u4eca\u65e5\u306f\u57fa\u672c\u7684\u306b\u30a6\u30a7\u30fc\u30d6\u30ec\u30c3\u30c8\u5909\u63db\u3068\u7d44\u307f\u5408\u308f\u305b\u3066\u30cf\u30a4\u30d6\u30ea\u30c3\u30c9\u30d7\u30ed\u30bb\u30b9\u3068\u3057\u3066\u306e\u307f\u691c\u8a0e\u3055\u308c\u3066\u3044\u307e\u3059\u3002 IFS\u306e\u30d7\u30ed\u30d1\u30c6\u30a3\u3092\u5c0e\u51fa\u3067\u304d\u308b\u3088\u3046\u306b\u3059\u308b\u306b\u306f\u3001\u6a5f\u80fd\u306e\u91cf\u304c\u8ffd\u52a0\u306e\u8981\u4ef6\u3092\u6e80\u305f\u3059\u5fc5\u8981\u304c\u3042\u308a\u307e\u3059\u3002\u901a\u5e38\u304b\u3089 ifs \u8a71\u3055\u308c\u3066\u3001\u3053\u308c\u3089\u306e\u8981\u4ef6\u306f\u6697\u9ed9\u306e\u3046\u3061\u306b\u53d7\u3051\u5165\u308c\u3089\u308c\u3066\u3044\u307e\u3059\u3002\u3053\u308c\u3089\u306e\u8981\u4ef6\u306f\u6b21\u306e\u3068\u304a\u308a\u3067\u3059        (adsbygoogle = window.adsbygoogle || []).push({});after-content-x4IFS\u304c\u6700\u7d42\u7684\u306b\u751f\u6210\u3055\u308c\u305f\u3053\u3068\u3001\u3064\u307e\u308a\u3001\u6700\u7d42\u7684\u306b\u4ed6\u306e\u95a2\u6570\u304c\u7e70\u308a\u8fd4\u3055\u308c\u308b\uff08\u53cd\u5fa9\uff09\u30ea\u30f3\u30af\u306b\u3088\u3063\u3066\u307e\u3068\u3081\u308b\u3053\u3068\u304c\u3067\u304d\u308b\u591a\u304f\u306e\u6a5f\u80fd\u304c\u542b\u307e\u308c\u3066\u3044\u307e\u3059\u3002 \u305d\u306e\u90e8\u5c4b m {displaystyle m} \u30e1\u30c8\u30ea\u30c3\u30af\u3092\u5099\u3048\u305f\u5b8c\u5168\u306a\u30e1\u30c8\u30ea\u30c3\u30af\u7a7a\u9593 d {displaystyle d} and and IFS\u306e\u3059\u3079\u3066\u306e\u6a5f\u80fd\u304c\u53cd\u30a2\u30af\u30c6\u30a3\u30d6\u306b d {displaystyle d} \u306f\u3002\u524d\u63d0\u6761\u4ef61.\u30b8\u30a7\u30cd\u30ec\u30fc\u30bf\u30fc\u304b\u3089\u3053\u308c\u3092\u8981\u6c42\u3059\u308b\u3060\u3051\u3067\u5341\u5206\u3067\u3059\u3002 \u3053\u308c\u3089\u306e\u72b6\u6cc1\u4e0b\u3067\u306f\u3001\u4e0d\u5909\u306e\u81ea\u5df1\u985e\u4f3c\u306e\u91cf\u304c\u3042\u308a\u307e\u3059 \u30d0\u30c4 \u2286 m {displaystyle xsubseteq m} \u3002 \u81ea\u5df1\u985e\u4f3c\u306e\u91cf\u306f\u901a\u5e38\u3001\u6574\u6570hausdorff\u5bf8\u6cd5\u3092\u6301\u305f\u305a\u3001\u305d\u306e\u5f8c\u30d5\u30e9\u30af\u30bf\u30eb\u3068\u3082\u547c\u3070\u308c\u308b\u305f\u3081\u3001\u6307\u5b9a ifs fractal \u3002\u307e\u305f\u3001IFS\u306e\u5b58\u5728\u3092\u8981\u6c42\u3059\u308b\u3053\u3068\u306b\u3088\u308a\u3001\u81ea\u5df1\u985e\u4f3c\u6027\u306e\u6982\u5ff5\u3092\u3055\u3089\u306b\u5b9a\u7fa9\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002 \u6570\u5b66\u7684\u306a\u89b3\u70b9\u304b\u3089\u3001 \u7e70\u308a\u8fd4\u3055\u308c\u308b\u6a5f\u80fd\u30b7\u30b9\u30c6\u30e0 \u7528\u8a9e\u304c\u76f4\u63a5\u9069\u7528\u3059\u308b\u3053\u3068\u3082\u793a\u5506\u3057\u3066\u3044\u308b\u3088\u3046\u306b\u30d0\u30ca\u30c3\u30b7\u30e5\u56fa\u5b9a\u30c9\u30c3\u30c8\u30bb\u30c3\u30c8\u3002\u3053\u308c\u306b\u3088\u308a\u30011\u3064\u306e\u4ee3\u308f\u308a\u306b\u3044\u304f\u3064\u304b\u306e\u6a5f\u80fd\u304c\u8003\u616e\u3055\u308c\u3001\u660e\u78ba\u306a\u56fa\u5b9a\u70b9\u306e\u4ee3\u308f\u308a\u306b\u3001\u4e0d\u5909\u3001\u307b\u3068\u3093\u3069\u304c\u30d5\u30e9\u30af\u30bf\u30eb\u3067\u3001\u90e8\u5206\u7684\u306a\u90e8\u5c4b\u306e\u91cf\u304c\u3042\u308a\u307e\u3059\u3002 m {displaystyle m} \u7d50\u679c\u3002 2\u6b21\u5143\u30e6\u30cb\u30c3\u30c8\u306e\u6b63\u65b9\u5f62\u306f\u901a\u5e38\u3001\u30a4\u30e9\u30b9\u30c8\u306b\u4f7f\u7528\u3055\u308c\u307e\u3059 m = [ 0 \u3001 \u521d\u3081 ] \u00d7 [ 0 \u3001 \u521d\u3081 ] {displayStyle M = [0,1] times [0,1]} \u30e6\u30fc\u30af\u30ea\u30c3\u30c9\u8ddd\u96e2\u3067\u9078\u3070\u308c\u307e\u3059\u3002 \u305d\u306e\u305f\u3081\u3001\u30b3\u30f3\u30d1\u30af\u30c8\u30e1\u30c8\u30ea\u30c3\u30af\u7a7a\u9593\u306e\u6709\u9650\u91cf\u306e\u6a5f\u80fd\u304b\u3089\u59cb\u3081\u307e\u3059 \uff08 m \u3001 d \uff09\uff09 {displaystyle\uff08m\u3001d\uff09} \u305d\u308c\u81ea\u4f53\uff1a F1\uff1a= { \u03d5 1\u3001 &#8230; \u3001 \u03d5 r\uff1a m \u2192 m } \u3001 {displaystyle {mathcal {f} _ {1}\uff1a= {phi _ _ {1}\u3001dots\u3001phi _ _ {r} colon mto m}\u3001} \u305d\u306e\u3046\u3061\u306e\u53ce\u7e2e\u5b9a\u6570\u304c\u3042\u308b\u3068\u4eee\u5b9a\u3057\u307e\u3059 0 < c < \u521d\u3081 {displaystyle 0 m \u3001 \u03d5 \u2208 F1\uff1a d \uff08 \u03d5 \uff08 \u30d0\u30c4 \uff09\uff09 \u3001 \u03d5 \uff08 \u3068 \uff09\uff09 \uff09\uff09 \u2264 c d \uff08 \u30d0\u30c4 \u3001 \u3068 \uff09\uff09 {displaystyle forall x\u3001yin m\u3001phi in {mathcal {f}} _ {1} :; d\uff08phi\uff08x\uff09\u3001phi\uff08y\uff09\uff09leq c\u3001d\uff08x\u3001y\uff09}} \u30a4\u30c6\u30ec\u30fc\u30b7\u30e7\u30f3\u3092\u901a\u3058\u3066\u8a2d\u5b9a\u3057\u307e\u3059 F\u521d\u3081 {displaystyle {mathcal {f}} _ {1}} IFS\u306b f {displaystyle {mathcal {f}}} \u7826\u3001\u305d\u3046\u3067\u3059 Fn+1\uff1a= F1\u2218 Fn\uff1a= { \u03d5 \u2218 f \uff1a \u03d5 \u2208 F1\u3001 f \u2208 Fn} {displaystyle {mathcal {f}} _ {n+1}\uff1a= {mathcal {f}} _ {1} circ {mathcal {f}} _ {n}\uff1a= {phi circ f\uff1a; phi in {mathcal {f}}} _ {1} _ {1 }} \u305d\u3057\u3066\u6700\u5f8c\u306b\u53d6\u5f97\u3057\u307e\u3059 F\uff1a= \u22c3 n=1\u221eFn{displaystyle {mathcal {f}}\uff1a= bigcup _ {n = 1}^{infty} {mathcal {f}} _ {n}}} \u3002 \u6587\uff1a \u3059\u3079\u3066\u95a2\u6570\u3067\u3059 \u03d5 1\u3001 &#8230; \u3001 \u03d5 r{displaystyle phi _ {1}\u3001dots\u3001phi _ _ {r}} \u306e F1{displaystyle {mathcal {f}} _ {1}} \u5951\u7d04\u7684\u306b\u306f\u3001\u4e0d\u5909\u30b5\u30d6\u30bb\u30c3\u30c8\u304c\u3042\u308a\u307e\u3059 \u30d0\u30c4 {displaystyle x} \u3001\u56fa\u5b9a\u70b9\u65b9\u7a0b\u5f0f \u30d0\u30c4 = \u22c3i=1r\u03d5i\uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle x = bigcup _ {i = 1}^{r} phi _ {i}\uff08x\uff09} \u6e80\u305f\u3059\u3002\u3053\u308c\u304c\u9069\u7528\u3055\u308c\u308b\u305f\u3081\uff1a \u305d\u308c\u305e\u308c\u306b f \u2208 F{displaystyle fin {mathcal {f}}} \u6b63\u78ba\u306b1\u3064\u306e\u56fa\u5b9a\u70b9\u304c\u3042\u308a\u307e\u3059\u3002\u4e0d\u5909\u91cf \u30d0\u30c4 {displaystyle x} \u3059\u3079\u3066\u306e\u56fa\u5b9a\u70b9\u306e\u91cf\u306e\u30c8\u30dd\u30ed\u30b8\u30ab\u30eb\u306a\u7d50\u8ad6\u3067\u3059 {x\u2208M|\u2203F\u2208F:x=F(x)}{displaystyle {xin m |; exists fin {mathcal {f}}\uff1a\u3001x = f\uff08x\uff09}}}} \u3002 \u306f \u3068 \u2208 m {displaystyle yin m} \u4efb\u610f\u306e\u30dd\u30a4\u30f3\u30c8\u3001\u6b21\u306e\u70b9\u306f\u3053\u306e\u30dd\u30a4\u30f3\u30c8\u306e\u8ddd\u96e2\u306b\u9069\u7528\u3055\u308c\u307e\u3059 d(X,F(y))\u2264cFd(X,y){displaystyle d\uff08x\u3001f\uff08y\uff09\uff09leq c_ {f}\u3001d\uff08x\u3001y\uff09} \u305d\u308c\u305e\u308c\u306e\u305f\u3081 F\u2208F{displaystyle fin {mathcal {f}}} \u3002 \u63a8\u5b9a\u5024\u304c\u9069\u7528\u3055\u308c\u307e\u3059 cF\u2264 cm{displaystyle c_ {f} leq c^{m}} \u3001\u6edd f {displaystyle f} \u4e00 m {displaystyle m}  &#8211; \u30d5\u30a9\u30fc\u30eb\u30c9\u30c1\u30a7\u30fc\u30f3 f \u2208 Fm{displaystyle fin {mathcal {f}} _ {m}} \u958b\u59cb\u95a2\u6570\u306f\u3067\u3059\u3002 \u305d\u308c\u3067\u3067\u304d\u307e\u3059 \u30d0\u30c4 {displaystyle x} \u9650\u3089\u308c\u305f\u91cf\u306e\u53cd\u5fa9\u306b\u3088\u308a X0\u2282M,Xn+1=\u22c3i=1r\u03d5i(Xn){displaystyle x_ {0}\u30b5\u30d6\u30bb\u30c3\u30c8M\u3001quad x_ {n+1} = bigcup _ {i = 1}^{r} phi _ {i}\uff08x_ {n}\uff09} \u540c\u69d8\u306b\u8fd1\u4f3c\u3059\u308b\u3053\u3068\u3082\u3067\u304d\u307e\u3059\u3002 \u6587\u306f\u3001\u30e1\u30c8\u30ea\u30c3\u30af\u7a7a\u9593\u304b\u3089\u306e\u3082\u306e\u3067\u3042\u308b\u3068\u3044\u3046\u4e8b\u5b9f\u306b\u3088\u3063\u3066\u8a3c\u660e\u3055\u308c\u3066\u3044\u307e\u3059 \uff08 m \u3001 d \uff09\uff09 {displaystyle\uff08m\u3001d\uff09} \u65b0\u3057\u3044\u90e8\u5c4b\u3092\u5efa\u8a2d\u3057\u307e\u3057\u305f\u3002 m {displaystyle m} \u305d\u308c\u306f\u3002\u3053\u306e\u7a7a\u9593\u3068\u30a4\u30e9\u30b9\u30c8\u306e\u89b3\u70b9\u304b\u3089\u3001\u3053\u308c\uff08Hausdorff\u30e1\u30c8\u30ea\u30c3\u30af\uff09\u306e\u30e1\u30c8\u30ea\u30c3\u30af\u3092\u5b9a\u7fa9\u3067\u304d\u307e\u3059 \u30d0\u30c4 \u21a6 \u22c3 \u79c1 = \u521d\u3081 r \u03d5 \u79c1 \uff08 \u30d0\u30c4 \uff09\uff09 {displaystyle xmapsto bigcup _ {i = 1}^{r} phi _ {i}\uff08x\uff09} \u53ce\u7e2e\u3067\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u30d0\u30ca\u30c3\u30b7\u30e5\u306e\u56fa\u5b9a\u70b9\u304c\u4f7f\u7528\u3067\u304d\u307e\u3059\u3002 \u30ab\u30aa\u30b9\u30b2\u30fc\u30e0 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u30d5\u30e9\u30af\u30bf\u30eb\u91cf\u306e\u5f62\u72b6 \u30d0\u30c4 {displaystyle x} SO -CALLED\u306e\u3082\u306e\u3092\u901a\u3057\u3066\u3059\u308b\u3053\u3068\u304c\u3067\u304d\u307e\u3059 \u30ab\u30aa\u30b9\u30b2\u30fc\u30e0 \u8996\u899a\u5316\u3055\u308c\u307e\u3059\u3002\u521d\u3081\u306b\u56fa\u5b9a\u70b9 x\u2192{displaystyle {vec {x}}} \u304b\u3089 x\u2192= \u03d5 \u521d\u3081 \uff08 x\u2192\uff09\uff09 {displaystyle {vec {x}} = phi _ {1}\uff08{vec {x}}\uff09} \u3053\u308c\u306b\u3064\u3044\u3066\u306f\u3001\u5b9a\u7fa9\u95a2\u6570\u3092\u30e9\u30f3\u30c0\u30e0\u306a\u9806\u5e8f\u3067\u8868\u793a\u304a\u3088\u3073\u4f7f\u7528\u3057\u307e\u3059\u3002\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3068\u3057\u3066\u3001\u3053\u308c\u306f\u6b21\u306e\u3088\u3046\u306b\u898b\u3048\u307e\u3059\u3002 100\u56de\u7d9a\u3051\u3066 x\u2192\uff1a= \u03d5 1\uff08 x\u2192\uff09\uff09 {displaystyle {vec {x}}\uff1a= phi _ {1}\uff08{vec {x}}\uff09} \u306b \u3042\u306a\u305f\u304c\u597d\u304d\u306a\u3060\u3051\u983b\u7e41\u306b\u30ea\u30d4\u30fc\u30bf\u30fc\u305f\u307e\u305f\u307e\u9078\u629e\u3057\u3066\u304f\u3060\u3055\u3044 i\u2208{1,\u2026,r}{displaystyle iin left {1\u3001dots\u3001right}} \u9053 x\u2192:=\u03d5i(x\u2192){displaystyle {vec {x}}\uff1a= phi _ {i}\uff08{vec {x}}\uff09} \u306b \u30dd\u30a4\u30f3\u30c8\u3092\u63cf\u304d\u307e\u3059 x{displaystyle x} \u3002 \u6ce8\u91c8\uff1a \u30d5\u30e9\u30af\u30bf\u30eb\u91cf\u307e\u3067\u306e\u8ddd\u96e2\u304c\u3059\u3079\u3066\u306e\u30b9\u30c6\u30c3\u30d7\u306b\u3042\u308b\u305f\u3081\u3001\u6700\u521d\u306e\u76f2\u76ee\u7684\u306a\u53cd\u5fa9\u3067\u306f\u91cd\u8981\u3067\u306f\u3042\u308a\u307e\u305b\u3093\u3002 \u30d0\u30c4 {displaystyle x} \u524a\u6e1b\u3055\u308c\u307e\u3059\u3002 z\u3067\u3059\u3002 B.\u53ce\u7e2e\u5b9a\u6570 c = 0 \u3001 5 {displaystyle c = 0 {\u3001} 5} \u305d\u3057\u3066\u57fa\u672c\u91cf m {displaystyle m} 1024\u00d71024\u30d4\u30af\u30bb\u30eb\u3067\u793a\u3055\u308c\u3066\u3044\u308b\u30e6\u30cb\u30c3\u30c8\u30b9\u30af\u30a8\u30a2\u306f\u300112\u306e\u30d6\u30e9\u30a4\u30f3\u53cd\u5fa9\u5f8c\u306b\u30d4\u30af\u30bb\u30eb\u30b5\u30a4\u30ba\u306e\u4e0b\u3067\u30a8\u30e9\u30fc\u304c\u4f4e\u4e0b\u3057\u307e\u3057\u305f\u3002 \u5404\u95a2\u6570\u3092\u547c\u3073\u51fa\u3059\u53ef\u80fd\u6027\u304c\u3042\u308b\u5834\u5408\u3001\u3088\u308a\u826f\u3044\u8868\u73fe\u304c\u4e00\u822c\u7684\u306b\u9054\u6210\u3055\u308c\u307e\u3059 \u03d5 i{displaystyle phi _ {i}} \u306e\u30dc\u30ea\u30e5\u30fc\u30e0\u306b\u307b\u307c\u6bd4\u4f8b\u3057\u307e\u3059 \u03d5 i\uff08 m \uff09\uff09 {displaystyle phi _ {i}\uff08m\uff09} \u306f\u3002 \u518d\u5e30 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] \u30a2\u30d5\u30a3\u30f3\u30d5\u30e9\u30af\u30bf\u30eb\u306e\u5834\u5408\u3001\u3067\u304d\u308c\u3070\u30a2\u30d5\u30a3\u30f3\u30d5\u30e9\u30af\u30bf\u30eb\u306e\u5225\u306e\u53ef\u80fd\u6027\u306f\u3001 \u518d\u5165\u308a \u7fa4\u8846\u306e\u8fd1\u4f3c \u30d0\u30c4 {displaystyle x} \u3002\u3053\u308c\u306f\u901a\u5e38\u3001\u30b3\u30d4\u30fc\u3092\u4f7f\u7528\u3057\u3066\u9bae\u3084\u304b\u306b\u4f7f\u7528\u3057\u3066\u3044\u307e\u3059\u8aac\u660e\uff1a\u958b\u59cb\u753b\u50cf\u3067\u3055\u307e\u3056\u307e\u306a\u524a\u6e1b\u3092\u884c\u3044\u3001\u898f\u5247\u306b\u5f93\u3063\u3066\u3053\u308c\u3092\u4fee\u6b63\u3057\u307e\u3059\u65b0\u3057\u3044\u30b7\u30fc\u30c8\u3067\u3001\u6b21\u306e\u30b9\u30c6\u30c3\u30d7\u306e\u958b\u59cb\u753b\u50cf\u3068\u3057\u3066\u4f7f\u7528\u3057\u307e\u3059\u3002 \u307e\u305f \u30bf\u30fc\u30c8\u30eb\u30b0\u30e9\u30d5\u30a3\u30c3\u30af L\u30b7\u30b9\u30c6\u30e0\u306e\u69cb\u7bc9\u7528\u4f7f\u7528\u3055\u308c\u3001\u540c\u69d8\u306e\u30a2\u30a4\u30c7\u30a2\u306b\u5f93\u3044\u307e\u3059\u3002 \u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u3068\u3057\u3066\u3001\u518d\u5e30\u7684\u306b\u547c\u3073\u51fa\u3059\u6a5f\u80fd\u304c\u5fc5\u8981\u3067\u3059\u3002 f \uff08 n \uff09\uff09 = \u22c3 \u79c1 = \u521d\u3081 r \u03d5 \u79c1 \uff08 f \uff08 n  &#8211;  \u521d\u3081 \uff09\uff09 \uff09\uff09 {displaystyle f\uff08n\uff09= bigcup _ {i = 1}^{r} phi _ {i}\uff08f\uff08n-1\uff09\uff09} \u4efb\u610f\u306e\u91d1\u984d\u3067 f \uff08 0 \uff09\uff09 {displaystyle f\uff080\uff09} \u6c17\u304c\u3064\u3044\u305f\u3002\u5b9f\u88c5\u306b\u306f\u3001\u73fe\u5728\u306e\u5ea7\u6a19\u7cfb\u304c\u30a2\u30d5\u30a3\u30f3\u3068\u3057\u3066\u306e\u30b9\u30bf\u30c3\u30af\u30e1\u30e2\u30ea\u304c\u5fc5\u8981\u3067\u3059\u5ea7\u6a19\u5909\u63db\u304c\u8a18\u9332\u3055\u308c\u307e\u3059\u3002\u3053\u308c\u306b\u3088\u308a\u3001\u30a2\u30eb\u30b4\u30ea\u30ba\u30e0\u304c\u5f97\u3089\u308c\u307e\u3059  \u518d\u5e30\u306e\u6df1\u3055\u306e\u30b3\u30c3\u30db\u30d5\u30e9\u30af\u30bf\u30eb0\u301c5 f \u79c1 g \u306e r \uff08 n \uff09\uff09 {displaystyle figur\uff08n\uff09} \uff1a \u30d5\u30e9\u30af\u30bf\u30eb\uff1a \u30ab\u30d0\u30fc f \u79c1 g \u306e r \uff08 \u5341 \uff09\uff09 {displaystyle figur\uff0810\uff09} on\uff08\u4f8b\u3068\u3057\u306610\uff09 \u30a2\u30d5\u30a3\u30f3\u30a4\u30e9\u30b9\u30c8 [ \u7de8\u96c6 | \u30bd\u30fc\u30b9\u30c6\u30ad\u30b9\u30c8\u3092\u7de8\u96c6\u3057\u307e\u3059 ] IF\u306e\u751f\u6210\u6a5f\u80fd\u306f\u30012\u6b21\u5143\u306e\u30a2\u30d5\u30a3\u30f3\u753b\u50cf\u3067\u3059Unity Squary\u305d\u308c\u81ea\u4f53\u3002\u3059\u3079\u3066\u306e\u95a2\u6570 \u03d5 k {displaystyle phi _ {k}} 2\u00d72\u30de\u30c8\u30ea\u30c3\u30af\u30b9\u3067\u4e0e\u3048\u3089\u308c\u307e\u3059 a k {displaystyle a_ {k}} \u304a\u3088\u3073\u30b7\u30d5\u30c8\u30d9\u30af\u30c8\u30eb b k {displaystyle b_ {k}} \u3002 Koch Fractal\u306fZ\u3067\u3059\u3002 B.\u6b21\u306e2\u3064\u306e\u95a2\u6570\u306e\u30b7\u30b9\u30c6\u30e0\u306b\u3088\u3063\u3066\u751f\u6210\u3055\u308c\u307e\u3059\u3002 \u03d5 1(xy)= 13(cos\u206130\u2218sin\u206130\u2218sin\u206130\u2218\u2212cos\u206130\u2218)(xy){displaystyle phi _ {1} {binom {x} {y}} = {craud {1} {sqrt {3}}} {begin {pmatrix} cos 30^{circurs binom {x} {y}}}}} \u3001 \u03d5 2(xy)=  &#8211;  13(\u2212cos\u206130\u2218sin\u206130\u2218sin\u206130\u2218cos\u206130\u2218)(xy)+ 13(cos\u206130\u2218sin\u206130\u2218){displaystyle phi _ {2} {binom {x} {y}} =  &#8211;  {craud {1} {sqrt {3}}} {begin {pmatrix} -cos 30^{cir binom {x}} {y}} {3t {1} {1} {1} {1} {1}} {cos 30^{rivss \u30af\u30c3\u30af\u66f2\u7dda\u3092\u4f5c\u6210\u3059\u308b\u305f\u3081\u306e\u53e4\u5178\u7684\u306a\u65b9\u6cd5\u3067\u306f\u30014\u3064\u306e\u95a2\u6570\u304c\u4f7f\u7528\u3055\u308c\u307e\u3059 \u03d5 1\uff08 \u30d0\u30c4 \u3001 \u3068 \uff09\uff09 = \uff08 x3,y3\uff09\uff09 {displaystyle phi _ {1}\uff08x\u3001y\uff09= left\uff08{frac {x} {3}}\u3001{frac {y} {3}}\u53f3\uff09} \u03d5 2\uff08 \u30d0\u30c4 \u3001 \u3068 \uff09\uff09 = \uff08 2+x\u22123y6,3x+y6\uff09\uff09 {displaystyle phi _ {2}\uff08x\u3001y\uff09= left\uff08{frac {2+x- {sqrt {3}} y} {6}}\u3001{frac {sqrt {3}} x+y} {6}}}}}}}} \u03d5 3\uff08 \u30d0\u30c4 \u3001 \u3068 \uff09\uff09 = \uff08 3+x+3y6,3\u22123x+y6\uff09\uff09 {displaystyle phi _ {3}\uff08x\u3001y\uff09= left\uff08{frac {3+x+{sqrt {3}} y} {6}}\u3001{frac {sqrt {3}}  &#8211;  {sqrt {3}}} x+y} {6}}} \u03d5 4\uff08 \u30d0\u30c4 \u3001 \u3068 \uff09\uff09 = \uff08 2+x3,y3\uff09\uff09 {displaystyle phi _ {4}\uff08x\u3001y\uff09= left\uff08{frac {2+x} {3}}\u3001{frac {y} {3}}\u53f3\uff09} \u53f3\u5074\u306e\u30b7\u30a2\u30d4\u30f3\u30b9\u30ad\u30fc\u30c8\u30e9\u30a4\u30a2\u30f3\u30b0\u30eb\u306f\u306b\u3088\u3063\u3066\u751f\u6210\u3055\u308c\u307e\u3059 \u03d5 1\uff08 \u30d0\u30c4 \u3001 \u3068 \uff09\uff09 = \uff08 x2,y2\uff09\uff09 {displaystyle phi _ {1}\uff08x\u3001y\uff09= left\uff08{frac {x} {2}}\u3001{frac {y} {2}}\u53f3\uff09} \u03d5 2\uff08 \u30d0\u30c4 \u3001 \u3068 \uff09\uff09 = \uff08 x+12,y2\uff09\uff09 {displaystyle phi _ {2}\uff08x\u3001y\uff09= left\uff08{frac {x+1} {2}}\u3001{frac {y} {2}}\u53f3\uff09} \u03d5 3\uff08 \u30d0\u30c4 \u3001 \u3068 \uff09\uff09 = \uff08 x2,y+12\uff09\uff09 {displaystyle phi _ {3}\uff08x\u3001y\uff09= left\uff08{frac {x} {2}}\u3001{frac {y+1} {2}}\u53f3\uff09} 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