{"status":"ok","message-type":"work","message-version":"1.0.0","message":{"indexed":{"date-parts":[[2026,10,4]],"date-time":"2026-10-04T18:45:45Z","timestamp":1791139545444,"version":"4.1.0"},"reference-count":23,"publisher":"Association for Computing Machinery (ACM)","issue":"6","license":[{"start":{"date-parts":[[1982,6,1]],"date-time":"1982-06-01T00:00:00Z","timestamp":391737600000},"content-version":"vor","delay-in-days":0,"URL":"https:\/\/www.acm.org\/publications\/policies\/copyright_policy#Background"}],"content-domain":{"domain":["dl.acm.org"],"crossmark-restriction":true},"short-container-title":["Commun. ACM"],"published-print":{"date-parts":[[1982,6]]},"abstract":"<jats:p>A recurrent problem in generating realistic pictures by computers is to represent natural irregular objects and phenomena without undue time or space overhead. We develop a new and powerful solution to this computer graphics problem by modeling objects as sample paths of stochastic processes. Of particular interest are those stochastic processes which previously have been found to be useful models of the natural phenomena to be represented. One such model applicable to the representation of terrains, known as \u201cfractional Brownian motion,\u201d has been developed by Mandelbrot.<\/jats:p>\n                  <jats:p>The value of a new approach to object modeling in computer graphics depends largely on the efficiency of the techniques used to implement the model. We introduce a new algorithm that computes a realistic, visually satisfactory approximation to fractional Brownian motion in faster time than with exact calculations. A major advantage of this technique is that it allows us to compute the surface to arbitrary levels of details without increasing the database. Thus objects with complex appearances can be displayed from a very small database. The character of the surface can be controlled by merely modifying a few parameters. A similar change allows complex motion to be created inexpensively.<\/jats:p>","DOI":"10.1145\/358523.358553","type":"journal-article","created":{"date-parts":[[2002,7,27]],"date-time":"2002-07-27T07:34:59Z","timestamp":1027755299000},"page":"371-384","update-policy":"https:\/\/doi.org\/10.1145\/crossmark-policy","source":"Crossref","is-referenced-by-count":641,"title":["Computer rendering of stochastic models"],"prefix":"10.1145","volume":"25","author":[{"given":"Alain","family":"Fournier","sequence":"first","affiliation":[{"name":"Univ. of Toronto, Toronto, Ont., Canada"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Don","family":"Fussell","sequence":"additional","affiliation":[{"name":"Univ. of Texas, Austin"}],"role":[{"vocabulary":"crossref","role":"author"}]},{"given":"Loren","family":"Carpenter","sequence":"additional","affiliation":[{"name":"Lucasfilm, San Rafael, CA"}],"role":[{"vocabulary":"crossref","role":"author"}]}],"member":"320","published-online":{"date-parts":[[1982,6]]},"reference":[{"key":"e_1_2_1_1_2","doi-asserted-by":"publisher","DOI":"10.1016\/B978-0-12-079050-0.50012-6"},{"key":"e_1_2_1_2_2","doi-asserted-by":"publisher","DOI":"10.1145\/563858.563893"},{"key":"e_1_2_1_3_2","doi-asserted-by":"publisher","DOI":"10.1145\/800248.507101"},{"key":"e_1_2_1_4_2","volume-title":"Computer generated animated movie. First Showing at SIGGRAPH '80 (July","author":"Carpenter L.C.","year":"1980","unstructured":"Carpenter , L.C. Vol Libre . Computer generated animated movie. First Showing at SIGGRAPH '80 (July 1980 ). Carpenter, L.C. Vol Libre. Computer generated animated movie. First Showing at SIGGRAPH '80 (July 1980)."},{"key":"e_1_2_1_5_2","volume-title":"Proc. IEEE Conference on Computer Graphics, Pattern Recognition and Data Structure. (May","author":"Catmu U, E","year":"1975","unstructured":"Catmu U, E . Computer display of curved surfaces . In Proc. IEEE Conference on Computer Graphics, Pattern Recognition and Data Structure. (May 1975 ). CatmuU, E. Computer display of curved surfaces. In Proc. IEEE Conference on Computer Graphics, Pattern Recognition and Data Structure. (May 1975)."},{"key":"e_1_2_1_6_2","doi-asserted-by":"publisher","DOI":"10.1145\/360349.360354"},{"key":"e_1_2_1_7_2","doi-asserted-by":"publisher","DOI":"10.1145\/800249.807440"},{"key":"e_1_2_1_8_2","doi-asserted-by":"publisher","DOI":"10.1145\/800249.807458"},{"key":"e_1_2_1_10_2","doi-asserted-by":"publisher","DOI":"10.1016\/0146-664X(80)90008-8"},{"key":"e_1_2_1_11_2","doi-asserted-by":"publisher","DOI":"10.1145\/359842.359846"},{"key":"e_1_2_1_12_2","doi-asserted-by":"publisher","DOI":"10.1016\/B978-0-12-079050-0.50011-4"},{"key":"e_1_2_1_13_2","doi-asserted-by":"publisher","DOI":"10.1145\/358808.358815"},{"key":"e_1_2_1_14_2","first-page":"4","article-title":"and Van Ness, J.W. Fractional Brownian motions, fractional noises and applications","volume":"10","author":"Mandelbrot B.B","year":"1968","unstructured":"Mandelbrot , B.B . and Van Ness, J.W. Fractional Brownian motions, fractional noises and applications . SlAM Review , 10 , 4 , ( Oct. 1968 ), 422-437. Mandelbrot, B.B. and Van Ness, J.W. Fractional Brownian motions, fractional noises and applications. SlAM Review, 10, 4, (Oct. 1968), 422-437.","journal-title":"SlAM Review"},{"key":"e_1_2_1_15_2","doi-asserted-by":"publisher","DOI":"10.1029\/WR007i003p00543"},{"key":"e_1_2_1_16_2","doi-asserted-by":"publisher","DOI":"10.1017\/S0022112075003047"},{"key":"e_1_2_1_17_2","doi-asserted-by":"publisher","DOI":"10.1073\/pnas.72.10.3825"},{"key":"e_1_2_1_18_2","volume-title":"Form, Chance and Dimension","author":"Mandelbrot B.B.","year":"1977","unstructured":"Mandelbrot , B.B. Fractals : Form, Chance and Dimension . Freeman , San Francisco , ( 1977 ). Mandelbrot, B.B. Fractals: Form, Chance and Dimension. Freeman, San Francisco, (1977)."},{"key":"e_1_2_1_19_2","doi-asserted-by":"publisher","DOI":"10.1145\/800224.806820"},{"key":"e_1_2_1_20_2","first-page":"52","article-title":"Simulation of patterns of nature by computer graphics","volume":"74","author":"Mezei L.","unstructured":"Mezei , L. , Puzin , M. , and Conroy , P . Simulation of patterns of nature by computer graphics . Information Processing 74 , 52 - 56 . Mezei, L., Puzin, M., and Conroy, P. Simulation of patterns of nature by computer graphics. Information Processing 74, 52-56.","journal-title":"Information Processing"},{"key":"e_1_2_1_21_2","doi-asserted-by":"publisher","DOI":"10.1016\/0146-664X(80)90005-2"},{"key":"e_1_2_1_22_2","first-page":"139","article-title":"The problem of statistics of deadly quarrels","volume":"6","author":"Richardson L.F","year":"1961","unstructured":"Richardson , L.F . The problem of statistics of deadly quarrels . General Systems Yearbook , 6 , ( 1961 ), 139 - 187 . Richardson, L.F. The problem of statistics of deadly quarrels. General Systems Yearbook, 6, (1961), 139-187.","journal-title":"General Systems Yearbook"},{"key":"e_1_2_1_23_2","doi-asserted-by":"publisher","DOI":"10.1016\/0146-664X(79)90044-3"},{"key":"e_1_2_1_24_2","doi-asserted-by":"publisher","DOI":"10.1016\/0146-664X(80)90011-8"}],"container-title":["Communications of the ACM"],"original-title":[],"language":"en","link":[{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/358523.358553","content-type":"unspecified","content-version":"vor","intended-application":"text-mining"},{"URL":"https:\/\/dl.acm.org\/doi\/pdf\/10.1145\/358523.358553","content-type":"unspecified","content-version":"vor","intended-application":"similarity-checking"}],"deposited":{"date-parts":[[2025,6,17]],"date-time":"2025-06-17T12:37:55Z","timestamp":1750163875000},"score":1,"resource":{"primary":{"URL":"https:\/\/dl.acm.org\/doi\/10.1145\/358523.358553"}},"subtitle":[],"short-title":[],"issued":{"date-parts":[[1982,6]]},"references-count":23,"journal-issue":{"issue":"6","published-print":{"date-parts":[[1982,6]]}},"alternative-id":["10.1145\/358523.358553"],"URL":"https:\/\/doi.org\/10.1145\/358523.358553","relation":{"is-identical-to":[{"id-type":"doi","id":"10.1145\/280811.280993","asserted-by":"object"}]},"ISSN":["0001-0782","1557-7317"],"issn-type":[{"value":"0001-0782","type":"print"},{"value":"1557-7317","type":"electronic"}],"subject":[],"published":{"date-parts":[[1982,6]]},"assertion":[{"value":"1982-06-01","order":2,"name":"published","label":"Published","group":{"name":"publication_history","label":"Publication History"}}]}}