Teacher guide animation fractals


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Teacher guide animation fractals

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Teacher guide animation fractals

  1. 1. California Standards Addressed Code CCSS Math N-Q Number and Quantity – Quantities A-CED Algebra – Creating Equations Modeling Modeling G-MG Geometry – Modeling with Geometry G-SRT Geometry, Similarity, Right Triangles, and Trigonometry Strand CA Visual Arts Standard (Proficient) Creative Expression 2.1 Solve a visual arts problem that involves the effective use of the elements of art and principles of design 2.3 Develop and refine skill in the manipulation of digital imagery Historical and Cultural Context 3.2 Identify and describe the role and influence of new technologies on contemporary works of art Connections & Applications 5.4 Demonstrate an understanding of the various skills of an artist, art critic, art historian, art collector, art gallery owner, and philosopher of art (aesthetician).
  2. 2. Fractals are mysterious • A structure defined by fine and small scales and/or substructures • A structure demonstrating repetition and/or iteration (repetition of a process) • Shape cannot be defined by Euclidean geometry. • Infinitely complex (appear similar in all levels of magnification)
  3. 3. What is a fractal? • A fractal is an object that can be broken down into parts; each part is a reduced-size copy of the whole. This is called “self-similarity.”
  4. 4. What is self-similarity? • An object is self-similar if it is exactly (or approximately) similar to itself. • The means the whole object has the same shape as one or more of its parts.
  5. 5. Fractals can be simple or complex • A fractal is an object that can be broken down into parts; each part is a reduced-size copy of the whole. A Koch Curve fractal
  6. 6. Fractals can be simple or complex Sierpinski Carpet Fractal The Sierpinski carpet is a fractal first described by Waclaw Sierpinski in 1916.
  7. 7. Fractals are found everywhere
  8. 8. Fractals are found everywhere
  9. 9. Fractals are found everywhere
  10. 10. Fractals are found everywhere
  11. 11. Fractals are found everywhere
  12. 12. Fractals are found everywhere
  13. 13. Fractals are found everywhere
  14. 14. Fractals are found everywhere
  15. 15. Fractals are found everywhere
  16. 16. Fractals are found everywhere
  17. 17. Fractals are found everywhere
  18. 18. Fractals are found everywhere
  19. 19. Fractals are found everywhere http://paulbourke.net/fractals/googleearth/
  20. 20. Fractal Art
  21. 21. Where do we use fractals? • Many computer and digital game designers use fractals to create life-like imagery
  22. 22. Using Fractals to generate CGI
  23. 23. Using Fractals to generate CGI
  24. 24. Using Fractals to generate CGI The more complicated the fractal gets, the smoother (more realistic) the shape appears in CGI
  25. 25. Using Fractals to generate CGI
  26. 26. • In the following slides we will see some landscapes that are progressively more complex. These landscapes are NOT drawings. They are created entirely by a computer using “fractal interpolation.” • This is the procedure that is used by special effects artists to create computer generated scenes for the big screen. Fractal Landscapes From: https://goo.gl/y5DjFv
  27. 27. This is the crudest version. “Nature made of triangles.” From: https://goo.gl/y5DjFv
  28. 28. In this picture, the grid of triangles is a bit finer From: https://goo.gl/y5DjFv
  29. 29. The triangles are finer still and the mountains in the distance begin to look a bit better. From: https://goo.gl/y5DjFv
  30. 30. The next step. The mountains in the background look like real mountains. From: https://goo.gl/y5DjFv
  31. 31. Now we add some texture to the triangles. From: https://goo.gl/y5DjFv
  32. 32. Here we add some crude clouds and improve the landscape. From: https://goo.gl/y5DjFv
  33. 33. Here we add some crude trees, and improve the landscape and the clouds. From: https://goo.gl/y5DjFv
  34. 34. From: https://goo.gl/y5DjFv
  35. 35. Your project: • Synthesize what you know of squares, fractals, and animation to create an animated “fractal tiling.” Square Tiling Option 01 Sierpinski Carpet Square Tiling Option 02
  36. 36. Square Tiling and Sierpinski Carpet fractals Square Tiling Option 01 Sierpinski Carpet Square Tiling Option 02
  37. 37. Project How-To Video https://goo.gl/stIvN3 https://goo.gl/NgHnMb https://goo.gl/YLPOSg Difficulty: 1 Difficulty: 2Difficulty: 3 Square Tiling Option 01 Sierpinski Carpet Square Tiling Option 02
  38. 38. Project Exemplar and “Cheat Sheet”
  39. 39. Assessing Your Work