I've already observed how restrained Fibonacci rabbits are in their reproducton rate, due to the maturation delay (MD) of two months before producing their first offspring in the third. I've been constructing some of those well known family tree type diagrams for varying MD values: 1 month, 2 months (the Fibonacci case), 3 and 4. They seem to yield the following twelve-item sequences:
For MD = 1 month: 1 2 4 8 16 32 64 128 256 512 1024 2048 A simple doubling at each stage as every rabbit pair produces another in the second month of life. Fast.
2 months: 1 1 2 3 5 8 13 21 34 55 89 144
3 months: 1 1 1 2 3 4 6 9 13 19 24 31 The addition algorithm is a bit more complicated than for the familair Fibonacci one. It involves some leapfrogging (or should I say leapbunnying): 1 + 1 = 2, 1 + 2 = 3, 1 + 3 = 4, 2 + 4 = 6, 3 + 6 = 9, 4 + 9 = 13 and so on.
4 months: 1 1 1 1 2 3 4 5 7 10 14 19 Here we add each pair of numbers separated by two in between: 1 + 1 = 2, 1 + 2 = 3, 1 + 3 = 4, etc. Note that 10 is both the rabbit quantity and month number, just as 5 is for the Fibonacci case, so maybe the same sort of results as I observed before in "Fib 5".
OK I know my comments to Rachel's stimulating article have been proliferating like, well, you know what. That's just because they've been conceived and born with corresponding spontaneity.
I've already observed how restrained Fibonacci rabbits are in their reproducton rate, due to the maturation delay (MD) of two months before producing their first offspring in the third. I've been constructing some of those well known family tree type diagrams for varying MD values: 1 month, 2 months (the Fibonacci case), 3 and 4. They seem to yield the following twelve-item sequences:
For MD = 1 month: 1 2 4 8 16 32 64 128 256 512 1024 2048 A simple doubling at each stage as every rabbit pair produces another in the second month of life. Fast.
2 months: 1 1 2 3 5 8 13 21 34 55 89 144
3 months: 1 1 1 2 3 4 6 9 13 19 24 31 The addition algorithm is a bit more complicated than for the familair Fibonacci one. It involves some leapfrogging (or should I say leapbunnying): 1 + 1 = 2, 1 + 2 = 3, 1 + 3 = 4, 2 + 4 = 6, 3 + 6 = 9, 4 + 9 = 13 and so on.
4 months: 1 1 1 1 2 3 4 5 7 10 14 19 Here we add each pair of numbers separated by two in between: 1 + 1 = 2, 1 + 2 = 3, 1 + 3 = 4, etc. Note that 10 is both the rabbit quantity and month number, just as 5 is for the Fibonacci case, so maybe the same sort of results as I observed before in "Fib 5".
OK I know my comments to Rachel's stimulating article have been proliferating like, well, you know what. That's just because they've been conceived and born with corresponding spontaneity.
Chris G