Upcoming Classes

1. Upcoming Classes Tuesday, Sept. 4th Fractal Worlds & Chaotic Systems Assignments due: * Topic of first oral presentation or written paper * Read “Order in Pollock's Chaos”; Scientific American, December 2002 Thursday, Sept. 6th Motion, in the real world and in animated worlds Assignment due: * Read “It’s All in the Timing and the Spacing”, The Animator's Survival Kit, R. Williams, Pages 35-51 * Homework #2

2. Upcoming Deadlines Thursday, September 13th First draft of your first term paper or your oral presentation Thursday, September 27th First Set of Oral Presentations First term paper (if not giving presentation)

3. Oral Presentations The following persons will give oral presentations on Thursday, September 27th : • Batres, Adan • Boyd, Heidi • Chen, Emily • Kwiatkowski, Dajon • Lebedeff, Christopher • Lipton, Christopher For everyone else, your first term paper is due on that date.

4. Quiz Shortly after the Second World War, a new style of painting was popularized by American artists such as Jackson Pollock and Willem De Kooning. What is the name of their style?

5. Extra Credit: SF Museum of Art Visit San Francisco Museum of Modern Art and see Abstract Expressionist paintings. Turn in your ticket receipt ($7 for students). Worth one homework assignment ; deadline is Oct. 16th Guardians of the Secret, Jackson Pollock, 1943

6. Fractal worlds & Chaotic systems

7. The Evolution of Painting In 500 years painting in the Western world evolved Saint Cecilia and Eight Stories from her Life, Giotto(?), 1304 from this… Blue Poles 11, Jackson Pollock, 1952 … to this … What happened and what role has science played?

8. 14th and 15th Century The introduction of perspective during the Renaissance made paintings look much more realistic. Road to Calvary, Martini, 1315 The Annunciation, Botticelli, 1489

9. 16th and 17th Century Compositions become more varied; use of light and shadow is more sophisticated. Night Watch, Rembrandt, 1642 Diana and Callisto,Titian,1559

10. 18th and 19th Century Compositions are even more varied. The Orgy, William Hogarth, 1734 Turkish Bath, Ingres, 1862

11. Birth of Photography The first successful permanent photograph created by Nicephore Niepce in 1826. Photos become commonplace by 1850. Oldest surviving photograph, 1826 American Civil War photo, 1864

12. Impressionism in 19th Century Photographic detail less important than style. Starry Night, Van Gogh , 1889 Rouen Cathedral, Monet, 1894

13. Cubism & Surrealism in 20th Century Painters move further away from realism. The Persistence of Memory, Salvador Dali, 1931 Les Demoiselles d'Avignon, Picasso, 1907

14. Wassily Kandinsky Kandinsky was a pioneer of modern art in the early 1900’s Example of Kandinsky’s early work, Old Town II (1902)

15. An Accidental Discovery One evening Kandinsky walks into his studio and stunned by a beautiful painting that he doesn’t recognize. “First I hesitated, then quickly approached this mysterious picture, on which I saw nothing but shapes and colors…” He then realizes it’s one of his own paintings, upside-down. “I now knew fully well, that the object harms my paintings.” "Munich-Schwabing with the Church of St. Ursula”, 1908

16. Kandinsky's Composition VII (1913) Kandinsky and others begin to paint abstract forms

17. Abstract Expressionism Abstract Expressionism arises in America after the Second World war. It’s roots are in the abstract paintings of Kandinsky and the aggressive works of the German Expressionist movement. An example of German Expressionism (Self-Portrait as a Soldier, E.L. Kirchner, 1915) Composition, W. de Kooning,1955

18. Abstract Art Humor

19. Jackson Pollock In the late 1940’s, Pollock began to create paintings not in the traditional manner, on an easel with a brush, but by laying the canvas on the floor and pouring (some say dripping) the paint directly onto it.

20. Pollock’s One (1950)

21. Pollock’s Blue Poles 11 (1952)

22. Pollock?

23. Newly Discovered Pollocks In 2003, Alex Matter, whose parents were friends of Pollock, claimed to have discovered 24 paintings by Pollock among possessions that Matter’s father had left when he died in 1984. After the paintings were discovered, Mr. Matter consulted Ellen G. Landau, one of the world's most respected authorities on Pollock’s work. Prof. Landau declared the paintings to be authentic but others had doubts. But is this a genuine Pollock? In 1973, Blue Poles11 sold for two million dollars* so new Pollocks are worth a fortune. * Current value of Blue Poles 11 estimated at 150 million.

24. Pollock & Chaos In 1950 Time magazine quotes Italian critic Bruno Alfieri who describes Pollock's work as a manifestation of "chaos . . . absolute lack of harmony . . . complete lack of structural organization . . . total absence of technique, however rudimentary . . . once again, chaos." In a telegram to the editor Pollock will reply, "No chaos damn it!” Nov. 20, 1950 But could Pollock have understand what chaos is? Probably not since scientists only began to understand chaos in the 1970’s.

25. What is a Pollock? Is it random? Is it chaotic? Is it completely unstructured? Can we give scientific, measurable meaning to these questions? Yes! Let’s see how. Detail from Blue Poles 11 (1952)

26. Self-Similarity These three images appear similar. Leftmost is photo of an old wall, stripped of wallpaper, in Edgar Allan Poe’s house Other two are magnified views of the central section of the photo.

27. Exact and Statistical Self-Similarity Mathematical constructs, such as the ideal “tree” shown here, can have exact self-similarity at every possible scale.

28. Exact and Statistical Self-Similarity Mathematical constructs, such as the ideal “tree” shown here, can have exact self-similarity at every possible scale. In the natural world self-similarity is typically limited to a few scales and isn’t an exact duplicate at each scale. A real tree and the wallpaper have statistical self-similarity

29. Self-Similarity in Nature Notice how the oval shape of the plant and the segmentation of the branches is duplicated in each sub-branch, in each twig, even down to the individual leaves and their veins.

30. Self-similarity in Geology Is this cave large enough for a person to enter standing up?

31. Self-similarity in Geology It’s not a cave, it’s a small hole. Field of boulders? No, just rocks Geologists always place an object, such as their hammer, is such photos to establish the scale, which is impossible to determine otherwise due to self-similarity

32. Mathematical Constructions These images were designed using mathematics yet due to their self-similarity they have a natural appearance. Exactly self-similar fern Exactly self-similar coastline

33. Fractals The term fractal was coined in 1975 by Benoît Mandelbrot, an IBM mathematician. Fractals have (typically): • fine structure at all scales. • self-similar at all scales. • a non-integer dimension. • a natural appearance. Benoît Mandelbrot Self-similarity in the Mandelbrot set

34. Movie: The MandelBrot Set

35. Fractal-like Objects in Nature Clouds Vegetables Norway Coastlines Cracks

36. How Long is a Coastline? Depends on the size of your ruler; the shorter the ruler, the longer the coastline. Measuring the coastline of England 12x4=48 28x2=56 68x1=68

37. Box Counting Measuring coastline of Iceland Instead of using a ruler to find the length of an island’s coastline (which is its perimeter), we can lay a grid over a map of the island and count the number of boxes on the coast. Length of the coast is (Size of box, r) x (Number of boxes, N) In the three cases we get: (50)x(35) = 1750 kilometers (25)x(76) = 1900 kilometers (12.5)x(168) = 2100 kilometers Turns out that there is a pattern in these numbers. Iceland

38. 5 4 3 2 1 Fractal Exercise Use a CD to draw a circle on a sheet of graph paper. Count the number of large squares that are on the perimeter of the circle. Keep squares connected (no going diagonal) Count all the way around the circle; double check your count

39. Fractal Exercise Now count the number of small squares on the perimeter of the circle. Double check your count (OK to be off by one square). Next we’ll collect all the data in the class. 5 3 4 2 1

40. 5 4 3 2 1 Fractal Exercise Most of you should have found about 36 or 37 large squares and around 72-74 small squares. Notice that for a circle, when the size of the squares is halved, the number of squares is doubled. A circle is not a fractal, the perimeter has a circumference given by: p x (Diameter)

41. Dimension of a Circle For an object of dimension d, (Number of small boxes) = 2d x (Number of big boxes) For a circle, the number of small boxes is twice the number of big boxes so dimension is d = 1 Every simple curve has dimension d = 1 so they are not fractals

42. 5 4 3 2 1 Fractal Exercise (cont.) Now draw an organic-looking blob on a fresh sheet of graph paper. Count the number of big and small boxes, as you did for the circle. Everyone’s blob is different so everyone’s count will be different (but count carefully and double check the count).

43. 0.9808 Log( 80 ) – Log( 30 ) 1.4150 0.6931 Log( 2 ) Fractal Dimension To find the dimension of your blob, compute (Dimension) = --------------------------------- Log( # Small ) – Log( # Big ) Log( 2 ) For example: If the number of big boxes is 30 and the number of small boxes is 80 then (Dimension) = ----------------------------- = --------------- = In this example the blob is a fractal because its dimension, about 1.4, is between one and two.

44. Fractal Analysis of Pollock Start with a known Pollock

45. Fractal Analysis of Pollock Take a photo, then scan and digitize pieces.

46. Fractal Analysis of Pollock Lay down a grid of big boxes and count the filled boxes; repeat with small box grid. Big Boxes Small Boxes

47. Pollock’s Dimension This analysis was performed by R.P. Taylor and colleagues. They found that Pollock’s paintings are fractals. Painting destroyed By Pollock Early work Richard P. Taylor

48. Faking a Pollock Taylor tried to create fake drip paintings in Pollock’s style but couldn’t get the right fractal, self-similar structure.

49. Newly Discovered Pollocks?

50. Newly Discovered Pollocks? Taylor analyzed the newly discovered Pollock paintings and this February reported in Nature that there were "significant differences" between their patterns and those of known Pollock works. "Certainly my pattern analysis shouldn't be taken in isolation but should be integrated with all the known facts — including provenance, visual inspection and materials analysis," Taylor said. Several experts now believe that the paintings are not by Pollock and could in fact have been painted by more than one artist, possibly by Mercedes Matter and her art students, trying to imitate Pollock's technique.