{"id":6606,"date":"2013-01-10T14:30:11","date_gmt":"2013-01-10T19:30:11","guid":{"rendered":"https:\/\/www.bates.edu\/museum\/?page_id=6606"},"modified":"2019-12-04T13:30:17","modified_gmt":"2019-12-04T18:30:17","slug":"fractals-mapping-forms-in-nature","status":"publish","type":"page","link":"https:\/\/www.bates.edu\/museum\/education\/thousandwordproject\/lesson-plans\/fractals-mapping-forms-in-nature\/","title":{"rendered":"Fractals: Mapping Forms in Nature"},"content":{"rendered":"

The Thousand Words Project (Organization<\/a>),<\/a>\u00a0Catherine Cargile, Lewiston Middle School, 7th Grade Interdisciplinary<\/strong><\/h4>\n

“For me the most important instrument of thought is the eye.\u00a0 It sees similarities before a formula has been created to identify them.\u201d\u00a0\u00a0 -Benoit Mandelbrot<\/em><\/p>\n

Intro:<\/span><\/em><\/strong><\/p>\n

Overview:<\/strong>
\nStudents will discover the ways that fractal geometry interrelates artistic, scientific, and mathematical approaches to investigating natural forms, patterns and systems.<\/p>\n

Learning Goals<\/strong>:
\nStudents will develop an introductory concept of what a fractal is and how it relates to structures and forms in the natural world.\u00a0 (MLR Science A3, A4, E1)<\/p>\n

Students will become familiar with the mathematician Benoit Mandelbrot and his work developing fractal geometry. (MLR Science, C1, C2, C3)<\/p>\n

Students will be able to measure angles found in natural forms using a protractor. (MLR Science B1, Mathematics A3, C1)<\/p>\n

Students will be able to identify the use of different fractal forms in various artworks. (MLR Visual Arts D1, E1)<\/p>\n

Students will develop skills using concepts from fractal geometry, including iteration, self-similarity and scaling, to create natural forms using ink and a variety of brush techniques. (MLR Visual Arts B3, C1)<\/p>\n

Questions:<\/strong>
\nWhat is a fractal?\u00a0 Where do we see fractal forms in nature?<\/p>\n

What does \u2018fractal dimension\u2019 mean?\u00a0 How can one measure a jagged, irregular shape?<\/p>\n

Who is Benoit Mandelbrot?\u00a0 What is his role in the development of fractal geometry?<\/p>\n

What role did computer graphics play in the development of fractal geometry?\u00a0 What is the \u2018Mandelbrot set\u2019?<\/p>\n

How has the artistic process contributed to our understanding of fractals in nature?<\/p>\n

Vocabulary:<\/strong><\/p>\n

Fractal\u00a0\u00a0\u00a0\u00a0\u00a0 Iteration\u00a0\u00a0\u00a0\u00a0\u00a0 Scaling\u00a0\u00a0\u00a0\u00a0\u00a0 Self-Similarity\u00a0\u00a0\u00a0\u00a0\u00a0 Irregular\u00a0\u00a0\u00a0\u00a0\u00a0 Pattern<\/p>\n

Transformation\u00a0\u00a0\u00a0\u00a0\u00a0 Substitution\u00a0\u00a0\u00a0\u00a0\u00a0 Repetition\u00a0\u00a0\u00a0\u00a0\u00a0 Branching\u00a0\u00a0\u00a0\u00a0\u00a0 Dimension<\/p>\n

Symmetry\u00a0\u00a0\u00a0\u00a0\u00a0 System\u00a0\u00a0\u00a0\u00a0\u00a0 Equation\u00a0\u00a0\u00a0\u00a0\u00a0 Texture\u00a0\u00a0\u00a0\u00a0\u00a0 Angle\u00a0\u00a0\u00a0\u00a0\u00a0 Degree<\/p>\n

Images<\/strong>:<\/p>\n

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Utagawa Kuniyoshi<\/strong> (1797-1861, Japanese)
\nDragon Over Waves<\/em>,
\nca. 1830, Woodcut, 15 3\/4 x 10 1\/4, ,Gift of Weston and Mary Naef, 1994,
\n1994.24.34a<\/p>\n

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John Haegan, Eames<\/strong> – American
\nTwiggy<\/em>
\n1969, Etching, 1992.1.20<\/p>\n

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John Haegan Emaes<\/strong> – American
\nLittle Orange Tree<\/em>
\n1973, Etching, 1992.1.23<\/p>\n

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Sigmund, Abeles<\/strong> – American
\nWinter Tree<\/em>
\n1960, Woodcut, two color, 1995.5.<\/p>\n

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Carol Bates<\/strong> – American
\nConch Shell<\/em>
\n1947, Watercolor, 1959.1.2<\/p>\n

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Tadensz Jackowski
\n<\/em><\/strong>Matka-natura II<\/em> \u2013 Polish
\n1978, Etching, 1986.5.1<\/p>\n

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John Heagan Eames<\/strong>
\nVenetian Reverie<\/em>
\n1960, Etching, 1992.1.39<\/p>\n

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Chen Gin-ye<\/strong>
\nPink Flowers with Butterfy<\/em>
\n1998, Brush Painting, 1998.14.2<\/p>\n

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Chen Gin-ye<\/strong>
\nBranches with Red Blossoms<\/em>
\n1998, Brush Painting, 1998.14.3<\/p>\n

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Wilson Bentley<\/strong>
\nSnow Crystals<\/em>
\nc. 1920, Gelatin Silver Print, 2005.12.4<\/p>\n

Teach It:<\/span><\/em><\/strong><\/p>\n

Materials:<\/strong><\/p>\n