Solution to Challenge 2

Counting the petal folds and creases
1. A bird base has two petal folds, one on the front layer and one on the back.
2. Each petal fold uses three creases: two kite creases (the lower edges folded in to the centre line) and one hinge crease across the top. Open the base out and you should find those creases on both sides of the paper.
3. The total is therefore two petal folds and six petal creases, on top of the creases of the preliminary base.

Changing the script

t = 0.1
for n in range(1, 10):
    print('Folds', n, '-> layers', 2**n, '-> stack', round(2**n*t, 2), 'mm')

Output when run:

Folds 1 -> layers 2 -> stack 0.2 mm
Folds 2 -> layers 4 -> stack 0.4 mm
Folds 3 -> layers 8 -> stack 0.8 mm
Folds 4 -> layers 16 -> stack 1.6 mm
Folds 5 -> layers 32 -> stack 3.2 mm
Folds 6 -> layers 64 -> stack 6.4 mm
Folds 7 -> layers 128 -> stack 12.8 mm
Folds 8 -> layers 256 -> stack 25.6 mm
Folds 9 -> layers 512 -> stack 51.2 mm

The stack first goes beyond 10 mm at 7 folds (12.8 mm). With 0.08 mm paper it was also 7 folds (10.24 mm), just barely, so thicker paper only moves the point a little: each fold doubles the stack, so a small change in thickness makes very little difference to the number of folds.

Checkpoint: two petal folds, three creases each, six petal creases in all.