fractal

Etymology

It is borrowed from French fractal,^[2][3][4] also written fractale,^[5][6] coined by the mathematician Benoit Mandelbrot in “Les Objets Fractals” (1975).^[3][2][6] It is formed from Latin frāctus (“broken, uneven”), the past participle of frangō (“to break”),^[5][2][3] and the suffix -al,^[5][2] and the Latin verb is from Proto-Indo-European *bhreg- (“to break”), the root of break.^[3][5] Fraction comes from the same verb.^[4][7]

Earliest recorded meaning

A mathematically defined curve any small part of which, when enlarged, has the same statistical character as the original: 1975, in the November issue of Scientific American.^[2][5]

Semantic evolution

Mandelbrot wanted a word for the spatial patterns of nature that are so irregular or fragmented that classical geometry hardly helps in describing them, and proposed "a family of shapes I propose to call fractals — or fractal sets".^[3] The word is frequently used attributively or as an adjective.^[2][7] Later dictionaries widen it from a curve to a figure, surface or physical structure,^[7][8][6] and the American Heritage Dictionary notes its use in computer modelling of irregular patterns found in nature.^[9]

Timeline

• 1975 – a curve whose small parts, enlarged, have the statistical character of the whole; also as an adjective.^[2][5][3]
• 1977 – fractal sets, in Mandelbrot's Fractals.^[3]

Meanings

Noun

1. A curve, figure or surface any part of which, when magnified or reduced, resembles the whole or has the same statistical character.^[5][7][2]
2. A figure produced by repeatedly subdividing a simpler polygon or polyhedron according to an iterative process.^[8]
3. A pattern repeated at ever smaller scales, giving irregular shapes that classical geometry can't represent, as used in computer models of natural structures.^[9]
4. (physics) A structure with an irregular or fragmented shape at all scales between a greatest and a smallest.^[6]

Adjective

1. Of, relating to or having the nature of a fractal: fractal geometry.^[8][7]

Related words

• fraction
• fracture
• fragment
• break

References

1. ^ Wiktionary, the free dictionary, https://en.wiktionary.org
2. ^ a b c d e f g h Oxford English Dictionary Online (accessed March 2026), Oxford: Oxford University Press
3. ^ a b c d e f g Harper, Douglas. Online Etymology Dictionary, https://www.etymonline.com
4. ^ a b The American Heritage Dictionary of the English Language (online 2024), 5th ed., Boston: Houghton Mifflin Harcourt
5. ^ a b c d e f g Merriam-Webster Unabridged Dictionary (2024), online ed., Springfield, Mass.: Merriam-Webster
6. ^ a b c d Dictionary.com Unabridged (2016), based on the Random House Unabridged Dictionary, New York: Random House
7. ^ a b c d e Shorter Oxford English Dictionary on Historical Principles (2002), 5th ed., ed. William R. Trumble and Angus Stevenson, Oxford: Oxford University Press
8. ^ a b c Collins English Dictionary (2023), Glasgow: HarperCollins
9. ^ a b The American Heritage Dictionary of the English Language (2000), 4th ed., Boston: Houghton Mifflin