part7

Project a – Doubling allowances

Would you take out trash to the curb for pickup for one penny a month? I would, if my parents agree to double it every month! In other words, one penny for the first month, two for the second, four for the third month, and so on, as shown in the table A. It is really iterating function (1) every month by the function diagram as follows;

You may complete the “Pennies earned” columns by doubling the previous entry. As you see, after 10 months your allowance is about the minimum wage in 1999. On the 16^th month your allowance is over $300, and at the end of two years most parents can’t afford your expensive trash takeout services.

Table A. Doubling allowances over 24 months

No. of months	Pennies earned	No. of months	Pennies earned
1	1 = 2 ⁰	13
2	2 = 2 ¹	14
3	4 = 2 ²	15
4		16	32,768 = 2¹⁵
6		17
5		18
7		19
8		20
9		21
10	512 = 2⁹	22
11		23
12		24	8,388,608 = 2²³

Return to main text

Project b – Binary trees

Note:
Prog #1 is available for download on the index page.
If you use a Macintosh, view the Flash version.

You can grow the binary tree of figure 11 up to the tenth branching with the program Prog #1 which involves two parameter values

The scale factor

The angle

In fact, the binary tree of Prog #1 is based on the following construction scheme which is identical to figure 11 for a and , and permits a gradual tree growth for scaling factor a in the range of (1.2, 1.8).

Figure 11. A binary tree

You first step through successive branching by 2, 4, 8, 16, 32,..., and there are in all 1024 branches at the tenth branching. Afterwards, you may select your own parameter values for a and . We however suggest initially changing one of the parameters at a time. First, under you vary the angle by

= 20, 40, 60, 80, and 90.

Then, with = 45 fixed you vary the scale factor by

a = 1.2, 1.4, 1.6, and 1.8.

Can you explain the changes brought about by the parameter pair?

Return to main text