May
24
2011
The Game: computing growth
Posted by Vitalie CiubotaruPrevious posts on this topic:
- A[nother] strange idea: browser game
- The Game: progress (1)
- The Game: progress (2)
- The Game: progress (3)
- The Game: progress (4)
- The Game: progress (5)
- The Game: universality vs. specialization of players
- The Game: life and death
- The Game: plant types and species
* * *
1. Plant size
Under normal conditions, plant size increases over time. Plant growth depends on:
- Plant’s current size (
) — the larger the plant is, the more it adds every day.
- Growth rate (
) — a general concept, which will be discussed in more detail below.
- Cell size (
) — i.e. there is an upper limit for growth.
Thus, . When the plant is small, the upper limit is not important and the limiting factor is current size, so initially the plant grows [almost] exponentially. When the plant grows large, the upper limit becomes more binding and growth decelerates again. Let me solve this equation for
.
Solving the left side integral:
So
Solving the right side integral:
Now putting it all together:
Simplify and redefine the constant:
Finally, making it discrete:
2. Growth rate
Time to discuss . The growth rate depends on:
- (mis)match between the “climate requirements” of a particular species and “climate” or “resource endowment” of a particular cell
- capacity to acquire resources — roots and leaves
For example, insufficient sunlight can be partly compensated by large leaves and insufficient minerals/water — by longer roots. Excessive resources will represent a small saving in roots/leaves, but will still be limiting the growth rate. As a possible way to make the impact of deficit and excess of resources to be symmetric, developing roots and leaves can cost no resources, just a mouse click and some waiting time. Have to think a bit on this.
December 23rd, 2015 at 23:57
The idea is awesome, at least it looks througly thought over.
Have you tried implementing it in the end or left as a theretical researh?
December 29th, 2015 at 01:00
Well, I tried writing up some code for it, but never went beyond designing a simple SQL database and a simple hex grid in PHP/HTML. What you see is all I have, no more than an idea. Anyway, I’m afraid the era of browser games is over, and a new game is probably not even worth thinking about.
P.S.: Thanks for dropping by :-)