分形藝術程式設計

分形設計的絕版好書，作者之一是《演算法導論》中文版的翻譯者、南京大學電腦系博士生導師潘金貴教授。

目錄
§1.1 分形起源.............................................. .................................................. ................................1
1.1.1 分形現像很常見........................................... .................................................. ........1
1.1.2 "fractal"的由來.......................................... .................................................. ............2
1.1.3 "分形"的由來.......................................... .................................................. ..............5
1.1.4 分形與數學的關係.................................... .................................................. .....9
1.1.5 分形範例................................................ .................................................. ................10
§1.2 分形紀事.............................................. .................................................. ..................21
§1.3 分形概念.............................................. .................................................. ..................31
1.3.1 分形的定義...................................... .................................................. ...........31
1.3.2 作為認知方法的分形.................................... .................................................. 35
1.3.3 作為解釋工具的分形.................................... ................................................37
§1.4 分形維數............................................. .................................................. ................42
1.4.1 從拓樸維到度量維................................................ .................................................. ....42
1.4.2 自相似維度度量.................................... .................................................. .......47
1.4.3 Hausdoff維度度量........................................... .................................................. ....49
1.4.4 盒維度量..................................... .................................................. ..............51
§1.5 分形哲學.............................................. .................................................. ..................54
1.5.1 自然界中的分形現象.................................... .................................................54
1.5.2 分形現象與生成哲學.................................... .................................................56
§2.1 藝術的意義............................................. .................................................. ................59
2.1.1 藝術的意義............................................ .................................................. .............59
2.1.2 否定電腦藝術的觀點...................................... .....................................61
2.1.3 對否定觀點的反駁...................................... .................................................. ...64
§2.2 分形作為藝術............................................. .................................................. ................69
2.2.1 什麼叫分形圖形藝術.......................................... ................................................69
2.2.2 分形藝術的特色........................................... .................................................. ......73
§2.3 分形藝術在中國................................................ .................................................. ..............79
§2.4 分形藝術的生成方法........................................... .................................................. .......83
2.4.1 分形圖形的生成方法.................................... .................................................83
2.4.2 分形圖形的輸出與展示方法........................................ .....................................85
§2.5 分形藝術的發展前景................................................ .................................................. .......86
2.5.1 分形圖形的發展前景.................................... .................................................86
2.5.2 超大圖形與裝飾藝術.................................... .................................................87
2.5.3 分形藝術與新幾何學.................................... .................................................. 89
§3.1 計算機座標................................................ .................................................. ....................93
3.1.1 計算機不只計算........................................... .................................................. ..94
3.1.2 作業系統與檔案..................................... .................................................. ......95
3.1.3 電腦螢幕座標...................................... .................................................. ...101
§3.2 色彩與圖檔格式........................................... .................................................. ................103
3.2.1 孟塞爾標色體系及其他....................................... ........................................103
3.2.2 色彩與RGB值........................................... .................................................. .......106
3.2.3 CMYK分色片........................................... .................................................. .........109
3.2.4 圖形檔案的格式........................................... .................................................. ....110
§3.3 圖形初始化................................................ .................................................. ..................114
§3.4 函數遞歸分形圖形................................................ .................................................. ........121
3.4.1 渦旋曲線............................................ .................................................. ...........121
3.4.2: Koch曲線............................................ .................................................. ..........122
§3.5 產生元分形圖形...................................... .................................................. ...........123
3.5.1 生成元每段線段長度相同........................................ .....................................123
3.5.2 產生元每段線段長度不相同....................................... ................................130
3.5.3 生成元每段線段長度與旋轉方向不相同.................................... ................137
§3.6 不動點映射分形圖形.................................... .................................................. ......138
§3.7 圖案映像分形圖形................................................ .................................................. ........144
§4.1 Cantor三分集................................................ .................................................. ................149
§4.2 Peano曲線與Hilbert曲線................................................ .................................................. .153
§4.3 Koch曲線.............................................. .................................................. ....................160
§4.4 Sierpinski地毯.............................................. .................................................. ..............163
§4.5 Durer五邊形............................................ .................................................. ................174
§5.1 樹木曲線........................................ .................................................. ................177
§5.2 以線段為構成元素的圖形.................................... ................................................180
§5.3 以圓為構成元素的圖形.................................... .................................................. ...184
§5.4 以多邊形為構成元素的圖形.................................... ................................................190
§5.5 以星形為構成元素的圖形........................................ .................................................. 193
§6.1 林氏系統................................................ .................................................. ......................199
§6.2 實例與偽碼............................................ .................................................. ................201
§6.3 L系統資料表................................ .................................................. ..................209
§6.4 迭代函數系統............................................. .................................................. ................216
§6.5 擴散置限凝聚模型........................................... .................................................. ................232
§7.1 複數運算與點列迭代................................................ .................................................. ......237
7.1.1 複數四則運算................................................ .................................................. .......237
7.1.2 複平面上的點列.................................... .................................................. ......244
7.1.3 預料不到的變動.......................................... .................................................. .....247
§7.2 Julia集合.............................................. .................................................. ......................251
§7.3 Mandelbrot集合........................................ .................................................. ..........263
§7.4 Julia集合解密................................................ .................................................. ................271
§7.5 高維度與高次情形........................................... .................................................. ...........279
7.5.1 高維度情形................................ .................................................. ...............279
7.5.2 高次情形................................................ .................................................. ...............281
7.5.3 廣義芒德勃羅集與茱麗亞集................................ ..................................282
§7.6 牛頓法求根............................................ .................................................. ................287
§7.7 發散區域的分類............................................ .................................................. ..........294
§8.1 一維邏輯斯蒂映射.................................... .................................................. ..........301
§8.2 里雅普諾夫指數.................................... .................................................. ..............307
§8.3 雙混沌映射................................................ .................................................. ................309
§8.4 標準映射........................................ .................................................. ................318
§8.5 埃農保面積映射................................................ .................................................. ...........324
§8.6 國王映射.............................................. .................................................. ....................327
§8.7 三翅鷹映射................................................ .................................................. ................334
§9.1 如何取得軟體............................................. .................................................. ................338