Transcript fibrabbits.ppt

Rabbits
Rabbits: Month 1
Month
Busy
Pairs
Young
Pairs
Total
Pairs
1
0
1
1
Rabbits: Month 2
Month
Busy
Pairs
Young
Pairs
Total
Pairs
1
2
0
0
1
1
1
1
Rabbits: Month 3
the first
birth
Month
Busy
Pairs
Young
Pairs
Total
Pairs
1
2
3
0
0
1
1
1
1
1
1
2
Rabbits: Month 4
the second
birth
Month
Busy
Pairs
Young
Pairs
Total
Pairs
1
2
3
4
0
0
1
1
1
1
1
2
1
1
2
3
Rabbits: Month 5
Two births:
The purple ones
are now old enough
Month
Busy
Pairs
Young
Pairs
Total
Pairs
1
2
3
4
5
0
0
1
1
2
1
1
1
2
3
1
1
2
3
5
Rabbits: Month 6
Month
Busy
Pairs
Young
Pairs
Total
Pairs
1
2
3
4
5
6
0
0
1
1
2
3
1
1
1
2
3
5
1
1
2
3
5
8
Rabbits: Month 7
QuickTi me™ and a
None decom pressor
are needed to see t his pict ure.
QuickTi me™ and a
None decom pressor
are needed to see t his pict ure.
QuickTi me™ and a
None decom pressor
are needed to see t his pict ure.
QuickTi me™ and a
None decom pressor
are needed to see t his pict ure.
QuickTi me™ and a
None decom pressor
are needed to see t his pict ure.
QuickTi me™ and a
None decom pressor
are needed to see t his pict ure.
Month
Busy
Pairs
Young
Pairs
Total
Pairs
1
2
3
4
5
6
0
0
1
1
2
3
1
1
1
2
3
5
1
1
2
3
5
8
7
5
8
13
QuickTi me™ and a
None decom pressor
are needed to see t his pict ure.
QuickTi me™ and a
None decom pressor
are needed to see t his pict ure.
QuickTi me™ and a
None decom pressor
are needed to see t his pict ure.
QuickTi me™ and a
None decom pressor
are needed to see t his pict ure.
QuickTi me™ and a
None decom pressor
are needed to see t his pict ure.
QuickTi me™ and a
None decom pressor
are needed to see t his pict ure.
QuickTi me™ and a
None decom pressor
are needed to see t his pict ure.
The number of new pairs produced depends on
how many pairs there were two months ago
3 pairs in
month 4
3 births in
month 6
Month
Busy
Pairs
Young
Pairs
Total
Pairs
1
2
3
4
5
6
0
0
1
1
2
3
1
1
1
2
3
5
1
1
2
3
5
8
|Births| = |Pairs| two months ago
Two months later: all grown up and ready to get busy
Month
QuickTi me™ and a
None decom pressor
are needed to see t his pict ure.
QuickTi me™ and a
None decom pressor
are needed to see t his pict ure.
QuickTi me™ and a
None decom pressor
are needed to see t his pict ure.
QuickTi me™ and a
None decom pressor
are needed to see t his pict ure.
QuickTi me™ and a
None decom pressor
are needed to see t his pict ure.
5 births in
month 7
QuickTi me™ and a
None decom pressor
are needed to see t his pict ure.
QuickTi me™ and a
None decom pressor
are needed to see t his pict ure.
Young
Pairs
Total
Pairs
1 0
2 0
3 1
4 1
5 pairs in
5
5 month 2
6 3
1
1
1
2
3
5
1
1
2
3
5
8
7
8
13
QuickTi me™ and a
None decom pressor
are needed to see t his pict ure.
Busy
Pairs
5
QuickTi me™ and a
None decom pressor
are needed to see t his pict ure.
QuickTi me™ and a
None decom pressor
are needed to see t his pict ure.
QuickTi me™ and a
None decom pressor
are needed to see t his pict ure.
QuickTi me™ and a
None decom pressor
are needed to see t his pict ure.
QuickTi me™ and a
None decom pressor
are needed to see t his pict ure.
Total rabbits = old rabbits + new births
The Fibonacci numbers
fn = fn-1 + fn-2
Month
Busy
Pairs
Young
Pairs
Total
Pairs
1
2
3
4
5
6
0
0
1
1
2
3
1
1
1
2
3
5
1
1
2
3
5
8
f1 = f2 = 1