CantorMesh
CantorMesh
CantorMesh[n]
给出表示第 n 步康托尔 (Cantor) 集的网格区域.
CantorMesh[n,d]
给出 d 维康托尔集的第 n 步.
更多信息和选项
- CantorMesh 亦称为康托尔尘.
- CantorMesh[n] 通过重复移除单位区间及后续单元的中间的三分之一产生. »
- CantorMesh[n] 等价于 CantorMesh[n,1].
- CantorMesh 和 MeshRegion 有同样的选项，更多选项如下所示：
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DataRange Automatic 产生的网格坐标的范围
范例
打开所有单元 关闭所有单元基本范例 (2)
CantorMesh[2]Table[RegionMeasure[CantorMesh[n]], {n, 5}]//RationalizeFindSequenceFunction[%, n]CantorMesh[1, 2]CantorMesh[1, 3]范围 (4)
选项 (13)
DataRange (1)
DataRange 允许指定产生的网格坐标的范围：
CantorMesh[1, 2]RegionBounds[%]CantorMesh[1, 2, DataRange -> {{0, 1}, {0, 2}}]RegionBounds[%]MeshCellHighlight (2)
MeshCellHighlight 允许指定突出显示部分 CantorMesh：
CantorMesh[0, 2, MeshCellHighlight -> {{1, All} -> Red, {0, All} -> Black}]CantorMesh[0, 2, MeshCellHighlight -> {{1, 2} -> {Thick, Red}, {1, 3} -> {Dashed, Black}}]CantorMesh[0, 2, MeshCellHighlight -> {Line[{3, 4}] -> {Thick, Red}, Line[{2, 4}] -> {Dashed, Black}}]MeshCellLabel (2)
MeshCellLabel 可用来标注部分 CantorMesh：
CantorMesh[0, 2, MeshCellLabel -> {0 -> "Index"}]CantorMesh[0, 2, MeshCellLabel -> {{1, 1} -> "x", {1, 2} -> "y"}]CantorMesh[0, 2, MeshCellLabel -> {Line[{1, 3}] -> "x", Line[{3, 4}] -> "y"}]MeshCellMarker (1)
MeshCellMarker 可用来为部分 CantorMesh 赋值：
CantorMesh[0, 2, MeshCellMarker -> {{0, 1} -> 1, {0, 2} -> 2, {0, 3} -> 3, {0, 4} -> 4}]用 MeshCellLabel 显示标记：
CantorMesh[0, 2, MeshCellMarker -> {{0, 1} -> 1, {0, 2} -> 2, {0, 3} -> 3, {0, 4} -> 4}, MeshCellLabel -> {0 -> "Marker"}]MeshCellShapeFunction (2)
MeshCellShapeFunction 可用来为部分 CantorMesh 赋值：
CantorMesh[0, 3, MeshCellShapeFunction -> {1 -> (Tube[#1, .1]&)}]CantorMesh[0, 3, MeshCellShapeFunction -> {{1, 2} -> (Tube[#1, .1]&)}]CantorMesh[0, 3, MeshCellShapeFunction -> {Line[{5, 7}] -> (Tube[#1, .1]&)}]MeshCellStyle (3)
MeshCellStyle 允许指定部分 CantorMesh 的样式：
CantorMesh[0, 2, MeshCellStyle -> {{1, All} -> Red, {0, All} -> Black}]CantorMesh[0, 2, MeshCellStyle -> {{1, 1} -> {Thick, Red}, {1, 2} -> {Dashed, Black}}]CantorMesh[0, 2, MeshCellStyle -> {Line[{1, 3}] -> {Thick, Red}, Line[{3, 4}] -> {Dashed, Black}}]CantorMesh[1, 2, MeshCellStyle -> {{2, All} -> Black, {2, 1} -> Red, {2, {2, 3}} -> Pink}]应用 (4)
Cantor 集是通过重复移除单位区间及后续单元的中间的三分之一产生的：
Column[{CantorMesh[0], CantorMesh[1], CantorMesh[2], CantorMesh[3]}]Row[{CantorMesh[0, 2], CantorMesh[1, 2], CantorMesh[2, 2]}, Spacer[60]]Row[{CantorMesh[0, 3], CantorMesh[1, 3], CantorMesh[2, 3]}, Spacer[60]]Table[RegionMeasure[CantorMesh[k]], {k, 5}]//RationalizeFindSequenceFunction[%, n]Table[RegionMeasure[CantorMesh[k, 2]], {k, 5}]//RationalizeFindSequenceFunction[%, n]Table[{k, RegionMeasure[CantorMesh[k, 3]]}, {k, 0, 3}]//RationalizeFindSequenceFunction[%, n]属性和关系 (4)
CantorMesh 总是输出 MeshRegion 的全部：
CantorMesh[3, 2]{MeshRegionQ[%], RegionDimension[%]}一维情况下，CantorMesh 由区间组成：
CantorMesh[2]MeshCells[%, RegionDimension[%]]CantorMesh[1, 2]MeshCells[%, RegionDimension[%]]CantorMesh[0, 3]MeshCells[%, RegionDimension[%]]Table[RegionMeasure[CantorMesh[n]] / 2, {n, 5}]//RationalizeFindSequenceFunction[%, i]Limit[Sum[%, {i, 1, n}], n -> Infinity]DataRange->range 等价于 RescalingTransform[{…},range]:
CantorMesh[1, 2, DataRange -> {{1, 2}, {1, 3}}, Frame -> True]box = TransformedRegion[CantorMesh[1, 2], RescalingTransform[{{0, 1}, {0, 1}}, {{1, 2}, {1, 3}}]];MeshRegion[box, Frame -> True]可能存在的问题 (1)
Wolfram Research (2017)，CantorMesh，Wolfram 语言函数，https://reference.wolfram.com/language/ref/CantorMesh.html.
文本
Wolfram Research (2017)，CantorMesh，Wolfram 语言函数，https://reference.wolfram.com/language/ref/CantorMesh.html.
CMS
Wolfram 语言. 2017. "CantorMesh." Wolfram 语言与系统参考资料中心. Wolfram Research. https://reference.wolfram.com/language/ref/CantorMesh.html.
APA
Wolfram 语言. (2017). CantorMesh. Wolfram 语言与系统参考资料中心. 追溯自 https://reference.wolfram.com/language/ref/CantorMesh.html 年