Amazing Plants - Maths Coursework.

To start with I did 2D ones, here is one with a wall (indicated by a black line) with layers of the plants, and each layer has a different colour.

2

3

4

5

6

7

8

So on day one (the pink one) the size is one square.

The next day, day 2 (the orange one) has 4 new Squares and 5 Total Squares and so on.

For example, day Six (the dark blue one) has 21 new Squares and 66 Total. Now I need to find a formula to work out Nth day.

While I was working out the results, I noticed something, each Corner has X2 in the formula.

X2

X4

X6

X8

E.g. The plant above has 2 corners, so the formula has X4 in it.

Here is the table for the "Amazing Plant" that's above,

Day

New

Total

2

5

6

3

9

5

4

3

28

5

7

45

6

21

66

The Formulas:

For the new: (DayX4)-3

For the total: Day+(Day-1)XDay.

Now I will go onto the one with only one corner:

2

3

4

5

6

7

8

Day

New

Total

2

3

4

3

5

9

4

7

6

5

9

25

6

1

36

The Formulas:

For the new: (DayX2)-1

For the total: Day Squared.