希爾伯特曲線

Multi tool use
希爾伯特曲線一種能填充滿一個平面正方形的分形曲線(空間填充曲線),由大衛·希爾伯特在1891年提出。
由於它能填滿平面,它的豪斯多夫維是2。取它填充的正方形的邊長為1,第n步的希爾伯特曲線的長度是2n - 2-n。
L系統記法:
- 變數: L, R
- 常數: F, +, -
- 公理: L
- 規則:
- L → − R F + L F L + F R −
- R → − L F + R F R + F L −
- F : 向前
- - : 右轉90°
- + : 左轉90°
外部連結
- https://web.archive.org/web/20051214033356/http://pmlab.iecs.fcu.edu.tw/~chh/PMLAB/Hilbert/ch_hilbert.html
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维基共享资源中相关的多媒体资源:希爾伯特曲線
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分形
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特性 |
分形维数
- Assouad 维数
- 关联维数
- 豪斯多夫维数
- 计盒维数
- 填充维数
- 拓撲維數
- 递归
- 自相似
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Barnsley fern
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迭代函数系统 |
- 巴恩斯利蕨葉
- 康托尔集
- 龍形曲線
- 科赫雪花
- 门格海绵
- 谢尔宾斯基地毯
- 謝爾賓斯基三角形
- 空間填充曲線
- T型方間
- 魏尔斯特拉斯函数
- 單峰映象
- 萊維C形曲線
- 希爾伯特曲線
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奇異吸子 |
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L系統 |
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逃逸時間分形 |
- 曼德博集合
朱利亚集合
- 李亞普諾夫分形
- 牛頓分形
- 燃燒巨輪分形
- 三角帽分形
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渲染技术 |
- Buddhabrot
- 轨迹陷阱
- Pickover 杆
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隨機分形 |
- 布朗运动
- 布朗樹
- 分形地形
- 擴散限制凝聚
- 萊維飛行
- 曼德尔盒
- 曼德尔球
- 逾滲理論
- 自避行走
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學者 |
- 格奥尔格·康托尔
- 费利克斯·豪斯多夫
- 加斯東·朱利亞
- 海里格·馮·科赫
- 保羅·皮埃爾·萊維
- 亞歷山大·李亞普諾夫
- 本華·曼德博
- 劉易斯·弗雷·理查森
- 瓦茨瓦夫·谢尔宾斯基
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其他相關 |
- “英國的海岸線有多長?”
- 以豪斯多夫維數排列的分形列表
- 《分形之美》 (1986)
- 分形艺术
- 《混沌学传奇》 (1987)
- 《大自然的分形几何学》 (1982)
- 分形压缩
- 仿射变换
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