Fractal and sequences applications.

1. Fractals are
everywhere in the
world around us,
even in our bodies ...
A fractal fern leaf by flickr user Paulo Henrique Zioli

2. TED Talks Ron Eglash: African fractals, in buildings and braids
http://www.ted.com/index.php/talks/view/id/198

6. The Rectangle ...
Draw a rectangle that measures 12 cm by 8 cm, and shade the inside of the
rectangle. Construct the midpoints of each side of the rectangle, and then draw
a quadrilateral by joining these points. Shade the quadrilateral white. Now
continue the process by finding the midpoints of the quadrilateral, drawing the
rectangle, and shading it the same colour as the first rectangle. Draw six
generations. (The initial rectangle is the first generation.)
(a) Find the total
shaded area.
(b) Find the total
unshaded area.

7. The Rectangle ... (b) Find the total
unshaded area.
(a) Find the total shaded area.

8. The Square ...
Create a fractal that begins with a large square 20 cm on each side. Each
pattern requires that the square be divided into four equally sized squares, that
the bottom-left square be shaded, and the process continues in the upper-right
square. Repeat the process four times.
(a) Find the total
shaded area.
(b) Find the total
unshaded area.

9. The Square ...
(b) Find the total unshaded area.
(a) Find the total shaded area.

10. A Fractal: The Koch Snowflake
All about the Koch Snowflake on wikipedia

11. The total perimeter of iteration 3, to the
nearest centimetre, will be ________.
The total perimeter of iteration 13, to the
nearest centimetre, will be ________.

12. People on Mars
A group of 100 astronauts is sent to Mars to colonize the planet. NASA
scientists have predicted that the population will increase by 12 percent every
20 years. Find the terms of the sequence for the first 100 years.
(a) Write a recursive formula for this sequence.
(b) Draw a graph of the sequence of populations over 100 years. Describe the
shape of the graph.
(c) Draw a graph of the sequence of populations over 300 years. Does the
graph still look the same as it did before?

13. Level of Medication
Anthony, a worker in a medical lab, has accidentally been exposed to bacteria
that cause the disease anthrax. The treatment he uses is the antibiotic Cipro,
which he must take every 12 hours. His body eliminates 75 percent of the
medication in 12 hours. The level of medication in his body should be around
24 mg, and never higher than 36 mg. How many milligrams of Cipro should
he take to maintain the proper level of medication in his body?