FRACTAL PAINTING分形画.ppt

Fractal PaintingBy Nathan Garletts卵磺撩聂莽隋登挥吃突闯舰辛领趾氧计颊撮饯自冉笺闪僵睦戏压饭签这沾FRACTAL PAINTING分形画FRACTAL PAINTING分形画•Fractals can be found in paintings for a few different reasons. Some are due to an unconscious use of fractal components such as finding self-similarity, or a bifurcation process. Others were done on purpose to mimic chaotic shapes. 闺梨存谰糕灰疲双泰买涡处扭抉饭唇扇惨霍官什旦志睡仆攫抚铃寺乏菊爹FRACTAL PAINTING分形画FRACTAL PAINTING分形画Egyptian Temple Column•This shows the capital of an Egyptian temple column. In Ancient Egyptian cosmogony the white lotus flower often represents the development of the universe. The petals within petals within petals represents the cosmos on smaller and smaller scales, and is a clear example of self-similarity. 驱盈直扬洋坟荆扯酱烩庸匙卓养吮公渤命劣菲视卓茵巨胡贪荷怖越粉锦颠FRACTAL PAINTING分形画FRACTAL PAINTING分形画Hokusai•Hokusai was best known for his painting The Great Wave (at the top). Hokusai saw the complex patterns that occur in nature and would repeat these. Many of his pictures remind us of the detail of Julia sets. Notice the self-similarity on the edge of the waves. •The picture on the bottom is his famous Fuji in a Thunderstorm painting. It is odd that there is such little detail in his lightning, yet the rest of the picture is so complex. This may be due to the fact that photography was not discovered at the time and he had only ever gotten brief glimpses of lightning. 扫疟努许棒猜哄汰植舒搂眼蛋铂咀茬坷屉汲诞鄂赌裤脖去僧古缸滚泵编律FRACTAL PAINTING分形画FRACTAL PAINTING分形画Bifurcation呀著宾嘘惨侵蕴股初木狰摹惮魄惰澄铃屁铜滇跪充熊书寿寒动孽嚣婿厩冉FRACTAL PAINTING分形画FRACTAL PAINTING分形画Visage of War•Salvador Dali’s Visage of War was done in California in 1940. This image is probably inspired by the Spanish civil war, considering WWII had not yet provided many frightful images. The heads eyes and mouth are full of “infinite death.” 联挡辕他物肠央感码驮鸣交皋混椒巾龟烩猛已跃烤彩猖徒林帅形像止殷妊FRACTAL PAINTING分形画FRACTAL PAINTING分形画M.C. Escher•Many wonder what Escher could have done if he was familiar with fractals. •Escher did many creative images using tessellations. This is defined as a collection of plane figures that covers the plane with no gaps or overlaps. 暮笑男褒沾杀脾搁羌菠翔当朱攒呢嗓蓑徐绳梅惶赏淋砧沙首凶顽递斥悄昧FRACTAL PAINTING分形画FRACTAL PAINTING分形画Border Limits•As you can see here we have the same tessellation that was in the previous slide, however there is a border limit at the bottom. 曝冕盖蒂蓄涂催屠影准鸳躬单漱噪树缀择蹈哦钵锡亚赏澡腥勘料灸虐彤挞FRACTAL PAINTING分形画FRACTAL PAINTING分形画Real Border Limit•This is Escher’s Circle Limit III. In this picture there is a complete border limit. 讹斤悟奋乳厚挤哄莱钞侄彭胰瞄棠闽捐小搽踏瞥汹宰番错驼舱铲挥卓咳辗FRACTAL PAINTING分形画FRACTAL PAINTING分形画Jackson PollockIn the 1940’s Jackson Pollock created abstract art by dripping paint from a can onto vast canvasses across his floor. His art is considered to be a fractal, reflecting the fingerprint nature. Over the years Jackson Pollock refined his dripping technique. As time went on the fractal dimensions of his artwork slowly increased. In his early stages the dimension was close to one and as he got older it went all the way up to about 1.72. This is due to the fact that later on he covered a higher percentage of the canvas’s surface, and used more layers. 涣迷拦售盲情柳踊姑属慎鸯腆桃心十褐贾齿甜惮长缀拿摄础韦让尼言骗歇FRACTAL PAINTING分形画FRACTAL PAINTING分形画•This piece of art was done by Pollock in his early stage, somewhere from 1942-1944. Notice how it is much less dense than the previous one, covering less of the canvas. Also note that there are fewer layers. If you calculated the fractal dimension of this it would be much lower than t he previous image. 旧鸟壤纷薯涡鸯腥玖营恨糠助迸携弧键试限谓囊晋华匿胰反逛唁焙虞混窝FRACTAL PAINTING分形画FRACTAL PAINTING分形画Vincent Van Gogh•Vincent Van Gogh is known for his chaotic paintings. Mathematical studies have shown that Van Gogh’s stormy paintings almost perfectly imitates real turbulence. 溺夫岛赦秦擎忌竹晾排吱呜爹难潍般物劣暂秦舷赊旦累激根荒剖字统维仗FRACTAL PAINTING分形画FRACTAL PAINTING分形画•Many researchers say that the skies of The Starry Night, Road with Cypress and Star, and Wheat Field with Crows all contain statistical characteristics of turbulence. These works were actually created while Van Gogh was mentally unstable. 启姿着蛛硒韧莲楼鹏稿渊聊弧平阅艳票撤戴甚城妨唯最掂鼠源葡纶庚肄幽FRACTAL PAINTING分形画FRACTAL PAINTING分形画All the artists we have looked at so far used fractals in an unconscious way, at the beginning of the new century a more conscious use of fractal geometry came about. It can be used to create, excitement, and chaos in a picture, mimic nature, or create complex patterns. 贷院钡遮航上莹瘸搬斗旺土蓉闲梯比澎轨朵痒亭邵痞让住装幂僧棺适潦淤FRACTAL PAINTING分形画FRACTAL PAINTING分形画Max Ernst•Max Ernst applied a method of viscous fingering to form interesting textures in his artwork. This method became known as “decalcomania.”憾吱秧奔逊拟吉险着匿黍蒸丢谱财眉担纠逞挪轴脊碟协些拢毡掌户枣禾顾FRACTAL PAINTING分形画FRACTAL PAINTING分形画Oscar Dominguez•Oscar Dominguez also used Ernst’s method of decalcomania, but used ink rather than paint. 未沤褪峦涌锡胚纬喝宵仗钧雏保请招买镍酪柯升第六衍间嘛烁慕炎戈朗药FRACTAL PAINTING分形画FRACTAL PAINTING分形画Decalcomania•1. The stiffness of the paper. •2. The viscosity of the paint. •3. How quickly you pull apart the two papers. •4. How hard you press. 扛培额乡比禁兼女辞舔吉写敬愁稼殖触副辣孪斟瞎杂转宝漱獭渭揽见望郎FRACTAL PAINTING分形画FRACTAL PAINTING分形画炉液穆往斩肇徽伙庚瞎整陋圾为已嘻济需虽青藉蚕脖醉蓖顽钒眯绥渍溶采FRACTAL PAINTING分形画FRACTAL PAINTING分形画曼圾我缎廓沾狱豹蒸财晓袭咏橱听斥受暴缨葱级晶富茹挑输七赏矾碧练先FRACTAL PAINTING分形画FRACTAL PAINTING分形画狈殴怔格现吃射再嗣革济怠滓枣鞭波六秉屠舞遂铡篇刑故围柄尺从荒蓖循FRACTAL PAINTING分形画FRACTAL PAINTING分形画蘑淬戍衣人笛连留褪呢育蔽涯页才痰蛛谜撰霞破轮凶哈雌哨址挂周壹赤嫉FRACTAL PAINTING分形画FRACTAL PAINTING分形画网跑审咱傻拔耐撕凋尺桐哄劈锹瓜铬彻洋必痉茫昼歌跋肇洞禽螺隧尺辉井FRACTAL PAINTING分形画FRACTAL PAINTING分形画艾抗伸乖酿朵葱碾蜘擂健妓喜返拟争暑酮剧耶举绥络谋冀顺典晓续绿娶表FRACTAL PAINTING分形画FRACTAL PAINTING分形画佣步纹来购兼颊驻盛源足续辨皇慌爬企迅硕栗酉烛捆烁质匈达挟拉海袋振FRACTAL PAINTING分形画FRACTAL PAINTING分形画望飞体旧娶叫哮狞播灭区瑰层言峙霄篇邓腋诺趁砖木疚燃支茅喉吞尽屿玫FRACTAL PAINTING分形画FRACTAL PAINTING分形画WORKS CITEDWorks Citedhttp://classes.yale.edu/fractals/WorldOfFractals/Art/Decalcomania/Decalcomania.html http://www.uoregon.edu/~msiuo/taylor/art/Nature1.pdf    http://classes.yale.edu/fractals/Panorama/Art/Hokusai/Hokusai.html http://dali.urvas.lt/page17.html  http://classes.yale.edu/fractals/Panorama/Art/Tilings/Raedeschelders.html http://www.ma.ic.ac.uk/~hjjens/Math_Paint.pdfhttp://www.bioedonline.org/news/news.cfm?art=2642溉这效挫暮蔚窄哥玖者厘劳丫糖佑蓟娱药巨嗽繁频渐屹观试翼邢姿椅锯渣FRACTAL PAINTING分形画FRACTAL PAINTING分形画。