See fractal dimension on Wiktionary
Download JSON data for fractal dimension meaning in All languages combined (5.3kB)
{
"forms": [
{
"form": "fractal dimensions",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "fractal dimension (plural fractal dimensions)",
"name": "en-noun"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"senses": [
{
"categories": [
{
"kind": "other",
"name": "English entries with incorrect language header",
"parents": [
"Entries with incorrect language header",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "other",
"name": "English entries with topic categories using raw markup",
"parents": [
"Entries with topic categories using raw markup",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "other",
"name": "English terms with non-redundant non-automated sortkeys",
"parents": [
"Terms with non-redundant non-automated sortkeys",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "other",
"name": "Greek terms with redundant script codes",
"parents": [
"Terms with redundant script codes",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "other",
"name": "Korean terms with redundant script codes",
"parents": [
"Terms with redundant script codes",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "other",
"name": "Russian terms with redundant script codes",
"parents": [
"Terms with redundant script codes",
"Entry maintenance"
],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Czech translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Finnish translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Greek translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Hungarian translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Korean translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Mandarin translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Russian translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"name": "Terms with Spanish translations",
"parents": [],
"source": "w"
},
{
"kind": "other",
"langcode": "en",
"name": "Fractals",
"orig": "en:Fractals",
"parents": [],
"source": "w"
},
{
"kind": "topical",
"langcode": "en",
"name": "Mathematical analysis",
"orig": "en:Mathematical analysis",
"parents": [
"Mathematics",
"Formal sciences",
"Sciences",
"All topics",
"Fundamental"
],
"source": "w"
}
],
"examples": [
{
"ref": "2005, John G. Holden, Gauging the Fractal Dimension of Response Times from Cognitive Tasks",
"text": "Conventional statistical analyses presuppose that intrinsic variability is white noise. White noise yields a jagged and irregular line with a fractal dimension of 1.5, because successive observations are statistically independent of each other. Its fractal dimension indicates the extent to which white noise occupies 2-D space. White noise is uncorrelated noise. By contrast, the successive observations of pink noise tend to be positively correlated. This results in a less jagged trial series, and lower fractal dimensions that fall in the interval between 1 and 1.5.",
"type": "quotation"
},
{
"text": "The perimeter of Britain measured in the first dimension yields infinity, and measured in the second dimension yields zero, so it has to be measured in a fractal dimension of approximately 1.25."
}
],
"glosses": [
"A dimension in which it is the most suitable to make measurements on a fractal set."
],
"hyponyms": [
{
"word": "capacity dimension"
},
{
"word": "correlation dimension"
},
{
"word": "Hausdorff dimension"
},
{
"word": "information dimension"
},
{
"word": "Lyapunov dimension"
},
{
"word": "Minkowski-Bouligand dimension"
}
],
"id": "en-fractal_dimension-en-noun-pzu4VJS1",
"links": [
[
"mathematical analysis",
"mathematical analysis"
],
[
"dimension",
"dimension"
],
[
"fractal",
"fractal"
]
],
"raw_glosses": [
"(mathematical analysis) A dimension in which it is the most suitable to make measurements on a fractal set."
],
"related": [
{
"word": "dimension"
},
{
"word": "fractal"
}
],
"topics": [
"mathematical-analysis",
"mathematics",
"sciences"
],
"translations": [
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "a dimension for making measurements on a fractal set",
"word": "分形維數"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "fēnxíng wéishù",
"sense": "a dimension for making measurements on a fractal set",
"word": "分形维数"
},
{
"code": "cs",
"lang": "Czech",
"sense": "a dimension for making measurements on a fractal set",
"word": "fraktální dimenze"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "a dimension for making measurements on a fractal set",
"word": "fraktaalidimensio"
},
{
"code": "el",
"lang": "Greek",
"roman": "morfoklasmatikí diástasi",
"sense": "a dimension for making measurements on a fractal set",
"tags": [
"feminine"
],
"word": "μορφοκλασματική διάσταση"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "a dimension for making measurements on a fractal set",
"word": "fraktáldimenzió"
},
{
"code": "ko",
"lang": "Korean",
"roman": "peuraekteol chawon",
"sense": "a dimension for making measurements on a fractal set",
"word": "프랙털 차원"
},
{
"code": "ru",
"lang": "Russian",
"roman": "fraktalʹnaja razmernostʹ",
"sense": "a dimension for making measurements on a fractal set",
"tags": [
"feminine"
],
"word": "фрактальная размерность"
},
{
"code": "es",
"lang": "Spanish",
"sense": "a dimension for making measurements on a fractal set",
"tags": [
"feminine"
],
"word": "dimensión fractal"
}
]
}
],
"word": "fractal dimension"
}
{
"forms": [
{
"form": "fractal dimensions",
"tags": [
"plural"
]
}
],
"head_templates": [
{
"args": {},
"expansion": "fractal dimension (plural fractal dimensions)",
"name": "en-noun"
}
],
"hyponyms": [
{
"word": "capacity dimension"
},
{
"word": "correlation dimension"
},
{
"word": "Hausdorff dimension"
},
{
"word": "information dimension"
},
{
"word": "Lyapunov dimension"
},
{
"word": "Minkowski-Bouligand dimension"
}
],
"lang": "English",
"lang_code": "en",
"pos": "noun",
"related": [
{
"word": "dimension"
},
{
"word": "fractal"
}
],
"senses": [
{
"categories": [
"English countable nouns",
"English entries with incorrect language header",
"English entries with topic categories using raw markup",
"English lemmas",
"English multiword terms",
"English nouns",
"English terms with non-redundant non-automated sortkeys",
"English terms with quotations",
"Greek terms with redundant script codes",
"Korean terms with redundant script codes",
"Quotation templates to be cleaned",
"Russian terms with redundant script codes",
"Terms with Czech translations",
"Terms with Finnish translations",
"Terms with Greek translations",
"Terms with Hungarian translations",
"Terms with Korean translations",
"Terms with Mandarin translations",
"Terms with Russian translations",
"Terms with Spanish translations",
"en:Fractals",
"en:Mathematical analysis"
],
"examples": [
{
"ref": "2005, John G. Holden, Gauging the Fractal Dimension of Response Times from Cognitive Tasks",
"text": "Conventional statistical analyses presuppose that intrinsic variability is white noise. White noise yields a jagged and irregular line with a fractal dimension of 1.5, because successive observations are statistically independent of each other. Its fractal dimension indicates the extent to which white noise occupies 2-D space. White noise is uncorrelated noise. By contrast, the successive observations of pink noise tend to be positively correlated. This results in a less jagged trial series, and lower fractal dimensions that fall in the interval between 1 and 1.5.",
"type": "quotation"
},
{
"text": "The perimeter of Britain measured in the first dimension yields infinity, and measured in the second dimension yields zero, so it has to be measured in a fractal dimension of approximately 1.25."
}
],
"glosses": [
"A dimension in which it is the most suitable to make measurements on a fractal set."
],
"links": [
[
"mathematical analysis",
"mathematical analysis"
],
[
"dimension",
"dimension"
],
[
"fractal",
"fractal"
]
],
"raw_glosses": [
"(mathematical analysis) A dimension in which it is the most suitable to make measurements on a fractal set."
],
"topics": [
"mathematical-analysis",
"mathematics",
"sciences"
]
}
],
"translations": [
{
"code": "cmn",
"lang": "Chinese Mandarin",
"sense": "a dimension for making measurements on a fractal set",
"word": "分形維數"
},
{
"code": "cmn",
"lang": "Chinese Mandarin",
"roman": "fēnxíng wéishù",
"sense": "a dimension for making measurements on a fractal set",
"word": "分形维数"
},
{
"code": "cs",
"lang": "Czech",
"sense": "a dimension for making measurements on a fractal set",
"word": "fraktální dimenze"
},
{
"code": "fi",
"lang": "Finnish",
"sense": "a dimension for making measurements on a fractal set",
"word": "fraktaalidimensio"
},
{
"code": "el",
"lang": "Greek",
"roman": "morfoklasmatikí diástasi",
"sense": "a dimension for making measurements on a fractal set",
"tags": [
"feminine"
],
"word": "μορφοκλασματική διάσταση"
},
{
"code": "hu",
"lang": "Hungarian",
"sense": "a dimension for making measurements on a fractal set",
"word": "fraktáldimenzió"
},
{
"code": "ko",
"lang": "Korean",
"roman": "peuraekteol chawon",
"sense": "a dimension for making measurements on a fractal set",
"word": "프랙털 차원"
},
{
"code": "ru",
"lang": "Russian",
"roman": "fraktalʹnaja razmernostʹ",
"sense": "a dimension for making measurements on a fractal set",
"tags": [
"feminine"
],
"word": "фрактальная размерность"
},
{
"code": "es",
"lang": "Spanish",
"sense": "a dimension for making measurements on a fractal set",
"tags": [
"feminine"
],
"word": "dimensión fractal"
}
],
"word": "fractal dimension"
}
This page is a part of the kaikki.org machine-readable All languages combined dictionary. This dictionary is based on structured data extracted on 2024-06-23 from the enwiktionary dump dated 2024-06-20 using wiktextract (1b9bfc5 and 0136956). The data shown on this site has been post-processed and various details (e.g., extra categories) removed, some information disambiguated, and additional data merged from other sources. See the raw data download page for the unprocessed wiktextract data.
If you use this data in academic research, please cite Tatu Ylonen: Wiktextract: Wiktionary as Machine-Readable Structured Data, Proceedings of the 13th Conference on Language Resources and Evaluation (LREC), pp. 1317-1325, Marseille, 20-25 June 2022. Linking to the relevant page(s) under https://kaikki.org would also be greatly appreciated.