How Changing the Number of Tiles at the Centre of a Pattern will Affect the Number of Border Tiles Needed
For my experiment I am going to investigate how changing the number of
tiles at the centre of a pattern, will affect the number of border
tiles I will need. I will do this to find patterns and a formula, to
link back to each set of patterns. Each formula will be tested by
using a larger border, but with the same number of centre tiles, this
will ensure my formula is correct. I will then try to find a general
formula, that will enable me to predict the border for any size centre
tiles. I will also do the same for the total tiles in the pattern.
Key
N ~ Pattern
B ~ Outer border tiles
T ~ Total Tiles
C ~ Centre Tiles
D ~ First difference
H ~ Height
W ~ Width
/ ~ x÷y
[IMAGE] ~ Prediction
For two centre tiles
Table 1:
Pattern: N
1
2
3
4
5
Border Tiles: B
6
10
14
18
22
+4 +4 +4 +4
B= 4N + 2
To get 4N at the start of the formula, you have to put the added outer
borders into a table ( see above ). Each pattern number is counted as
N and the squares in that outer most border is counted as B. These
numbers change as each outer border gets bigger. Every pattern number
with only centre tiles has no border, so it has not been included in
the sequence to make my formulae. You notice you add 4 each time so