# Difference between revisions of "topology"

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− | + | *[[jbocre: fractal|fractal]]:Pierre Abbat suggests the word frinyselcimde, which is a reference to the fact that some (most) fractals have a fractional Hausdorff dimension in excess of their topological dimension. (For most objects, the Hausdorff dimension is identical to topological dimension) [[jbocre: Jay Kominek|Jay Kominek]] suggests paursmitai and ci'urtolcne as other possibilities.See the short thread on the Lojban list where this originally came up: [http://groups.yahoo.com/group/lojban/message/7845 | |

+ | **] [[jbocre: cein|cein]] suggests rapli fancu. | ||

− | + | *** I think that that would serve as a lay explanation of fractal, but is a far cry from approximating the mathimatically rigid definition of fractal. In particular, 'fractal'ness applies to objects, not functions, as functions cannot have topological dimension. The fact that you can make fractals by the repetition of some functions is more of a defining property of the function in question, rather than of fractals. -jay | |

+ | **** ok, ''rapli fancu cartu'' then :) {cein} | ||

− | + | **** A function can exhibit the self-similarity and nondifferentiability required. Also, Hausdorff dimension is a strange concept and has little to do with the idea of an axis, or even an independent variable in an abstract state space, so I am not sure cimde is the right gismu. --xod'' | |

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## Revision as of 17:16, 4 November 2013

- fractal:Pierre Abbat suggests the word frinyselcimde, which is a reference to the fact that some (most) fractals have a fractional Hausdorff dimension in excess of their topological dimension. (For most objects, the Hausdorff dimension is identical to topological dimension) Jay Kominek suggests paursmitai and ci'urtolcne as other possibilities.See the short thread on the Lojban list where this originally came up: [http://groups.yahoo.com/group/lojban/message/7845
- ] cein suggests rapli fancu.

- I think that that would serve as a lay explanation of fractal, but is a far cry from approximating the mathimatically rigid definition of fractal. In particular, 'fractal'ness applies to objects, not functions, as functions cannot have topological dimension. The fact that you can make fractals by the repetition of some functions is more of a defining property of the function in question, rather than of fractals. -jay
- ok,
*rapli fancu cartu*then :) {cein}

- ok,

- I think that that would serve as a lay explanation of fractal, but is a far cry from approximating the mathimatically rigid definition of fractal. In particular, 'fractal'ness applies to objects, not functions, as functions cannot have topological dimension. The fact that you can make fractals by the repetition of some functions is more of a defining property of the function in question, rather than of fractals. -jay

- A function can exhibit the self-similarity and nondifferentiability required. Also, Hausdorff dimension is a strange concept and has little to do with the idea of an axis, or even an independent variable in an abstract state space, so I am not sure cimde is the right gismu. --xod