# Doubling time

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The doubling time of a particular self-replicating system is the amount of time it takes to "duplicate itself". Equivalently, doubling time is the amount of time it takes for the population of a particular kind of thing to double. (The "fast production" tag has a few comments on how to speed this up).

The term generation time is often used interchangeably with doubling time.

Which gives a shorter doubling time:

• each machine prints the parts for a single child, then spits them out for assembly, and then prints the parts for the next child, or
• each machine produces a "litter" by printing out all the parts for 2 or more children simultaneously

?

The "Moving towards production" post implies that a Mendel can print out all its own parts, at roughly 9 hours (?) per tray of parts x 4 trays of parts = 36 hours (?).

The Development:Mendel Apollo (see [1]) is a larger variant of a Mendel that can print all its own parts in a single tray of parts. Still 36 hours (?), but now we can let it run over the weekend rather than having to manually unload the parts every 9 hours.

The Mini-Mendel page claims the Mini-Mendel can "reproduce three times faster". It links to a Erik de Bruijn blog post that estimates about 15 hours to print out all the parts.

However, this is all *printing* time. It doesn't really count as the next generation until it has been assembled, calibrated, loaded with raw materials, and started printing out the next generation.

Assuming a sufficiently large number of humans are putting these machines together and using them to fab the next generation, it appears that a "slow" generation time of 1 week is possible with the current Mendel design, and a "fast" generation time of 1 day seems possible with only minor improvements to the Mini-Mendel design. (Some bacteria can double every 6 hours[2]).

As of 2010, the human population of the world is estimated to be almost 7,000,000,000. The world's largest city has less than 20 million inhabitants. The RepRap project began in the City of Bath England which has a population of about 84,000 including the University of Bath which has about 13,000 students.

Using the above very rough estimates, and assuming a sufficiently large number of humans who want a RepRap and can somehow organize themselves and obtain adequate quantities of raw materials, energy, and "vitamins" (computers, motors, etc.), we get:

``` "slow"   "fast"     generations     population
0        0          0               1 machine: initial RepStrap starts printing next-generation RepRap
1 week   1 day      1 generation    2 machines
2 weeks  2 days     2 generations   4 machines
3 weeks  3 days     3 generations   8 machines
...
13 weeks 13 days   13 generations   8 kibimachines
14 weeks 14 days   14 generations  16 kibimachines: more than enough for every student at the University of Bath
15 weeks 15 days   15 generations  32 kibimachines
16 weeks 16 days   16 generations  64 kibimachines
17 weeks 17 days   17 generations 128 kibimachines: more than enough for the entire population of Bath
...
25 weeks 25 days   25 generations  32 Mebimachines: more than enough for the entire population of the largest city on Earth
...
33 weeks 33 days   33 generations   8 Gibimachines: more than enough for the entire population of Earth.
```

This does *not* require any one person to work for 33 weeks on nothing but RepRaps. Perhaps every person receives a box containing 1 slightly-used RepRap and enough parts to build another RepRap, and works only a single week assembling those parts to build a second RepRap, using both RepRaps to print 3 more sets of parts, and then boxes up the results (2 repraps, 2 sets of parts) into 2 boxes and sends 2 other people a box identical to the box that person originally received.

Perhaps every person receives a box containing enough parts to build one RepRap, and works only single week assembling those parts to build their own personal RepRap, using it to print 2 more sets of parts, and then boxing up those 2 sets of parts into 2 boxes and sending 2 other people a box identical to the box that person originally received.

Some people prefer the term "exponential assembly" for this sort of thing, rather than "self-replication".[3]

So why doesn't everyone on Earth who wants one have one already?

## system of machines

It is still an open question whether the total cost (or total doubling time) of a self-replicating system is minimized with (a) a single machine that can build any of its parts, such as a high-speed high-precision CNC Mill, or (b) a system of a few machines that collectively can build any of their parts, each one optimized to do one limited thing (list of techniques) at higher speed or precision or lower cost (or all three) than a full CNC mill.

PhilosophyPage#2._Rapid_prototyping suggests that a "single machine" is somehow more "elegant".

CubeSpawn and RepLab and the essay on putting printers in perspective suggests that a group of machines, each one separately optimized to do one thing really well, can do things no one machine can do alone.