Gingerbread Man
Richard Francisco & Molly McKee
There are interesting investigations on recursive sequences that can be made using Excel.
(Excel file)
The following essay investigates some properties of the so-called ‘Gingerbread Man’ Sequence. The exploration is completed using Microsoft Excel to quickly calculate several hundred values of the sequence. The Gingerbread Sequence is interesting in that it is relatively easy to write an implicit formula for the sequence, but it is quite difficult to gain intuition into the workings of the sequence through Algebra. For instance, consider the following ‘seed value pairs’ that were input into the original sequence. (Try the pairs in the Excel file)
Figure 1 and Figure 3 show the images created when both values are negative.
Figure 2 and Figure 4 show the images created with the same values, only they are positive.
A
.5
.5
.5
.5
2
47
47
B
2355
3
7
235
323
.5
2362
Values
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Below are some points which we found interesting.
Notice how the concentration of the points changes as the values of A and B change.
Figure 1
A: -.1
B: -3.5
Figure 2
A: .1
B: 3.5
Figure 3
A: -.9
B: -3.5
Figure 4
A: .9
B: 3.5
Figure 5
A: .5
B: 3.5
Figure 6
A: 1
B: 3.5
Figure 7
A: 135
B: .5
