1. Section 6.1 Images Viewing a Gallery of Fractals. Look for patterns.

2. Question of the Day How can you convince your parents that you’re eating enough broccoli?

3. Real or fake?

4. The Sierpinski Triangle

5. How many Quackers do you see ?

6. The Fern

7. Julia Sets

8. Section 6.2 The Infinitely Detailed Beauty of Fractals How to create works of infinite intricacy through repeated processes. It’s not where we begin, it’s how we get there.

9. Question of the Day What do you need to know to predict the world’s population in the future?

10. Self-Similarity The characteristic of looking the same as or similar to itself under increasing magnification.

11. A process of repeated replacement. Koch’s Kinky Curve

12. A process of repeated replacement. Sierpinski Triangle

13. A process of repeated replacement. Menger Sponge

14. A process of repeated replacement. Barnsley’s Fern

15. More on the Sierpinski Triangle! The final bow…

16. The Chaos Game Whatever number you generate, move halfway from where you are toward that numbered vertex and make a dot. Then roll again to determine the next number… and repeat the process.

17. Section 6.3 Between Dimensions Can the Dimensions of Fractals Fall through the Cracks? Start with the simple and familiar. Look for patterns. Apply patterns to new settings.

18. Question of the Day How do you turn a triangle into a snowflake?

19. What is a dimension? 1-dimensional: A line segment 2-dimensional: A filled in square 3-dimensional: A solid cube 4-dimensional: ?

20. In search of a pattern… Original Object Dimension of the object Scaling Factor to Make a Larger Copy Number of Copies Needed to Build the Larger Copy Line Square Cube

21. Section 6.4 The Mysterious Art of Imaginary Fractals Creating Julia and Mandelbrot Sets by Stepping Out in the Complex Plane Don’t be afraid to look and think before you try to understand.

22. Question of the Day What’s the story behind this picture?

23. Julia Sets

24. Mandelbrot Sets

25. A process in the plane.

26. Review of Complex Numbers.

28. Visualizing Complex Numbers

29. What is a Mandelbrot Set? An object that captures information about the collection of all (a + bi) – Julia Sets.

30. Section 6.5 The Dynamics of Change Can Change Be Modeled by Repeated Applications of Simple Professes? The best predictors of where you will be are where you are now and which way you’re going.

31. Question of the Day How close is your calculator’s answer to the correct answer?

32. Repeat, Repeat, Repeat Start somewhere. Apply a process and get a result. Apply the same process to that result to get a new result. Apply the process again to the new result to get a newer result. Repeat patiently and persistently, forever.

33. Conway’s Game of Life 1.A living square will remain alive in the next generation if exactly two or three of the adjoining eight squares are alive in this generation; otherwise, it will die. 2.A dead square will come to life if exactly three of its adjoining eight squares are alive; otherwise, it will remain dead.

34. Play the Game of Life!

35. Patterns in types of Populations Explosion Extinction Stable Periodic Migratory

36. Population Density Population Density = The change in population density is the change from year n to n+1:

37. The Rate of Change of Population

38. Section 6.6 Predetermined Chaos How Repeated Simple Processes Result in Utter Chaos Keep alert for significance even in ridiculous ideas.

39. Question of the Day What is the dimension of a cloud?

40. Experiment 1.Type in a random number. 2.Multiply it by 180. 3.Hit the SIN key and write down your answer in the second column next two 2. Keep all decimal places. 4.Repeat steps 2 and 3 for each new number you generate. Continue to record your results until you have 25 numbers in the second column.

41. A variation on the experiment 1.Enter the exact same first decimal number as before and repeat the process five times. 2.Clear your calculator of the previous result. 3.For the sixth number use the fifth number rounded to six decimals places. 4.Now, repeat the process as before until you have 25 numbers in the second column.

42. Predicting Future Populations The Verhulst Model = population in year n = population for the next year.