# Is it possible to mathematically model the growth of plants?

Are there mathematical equations that represent/model the growth of plants? For example, if I have a Bellis perennis and I want to know how it develops in a given environment (Sun is shining, defined amount of water etc). How can one say if it grows a certain height and leafs and all other organs? I don't want a generic solution for this like using L-System and stuff, I just want to have a source where I can research growth rules for a given plant, flower or tree.

Background:
I'm making a kind of mini-game for a computer-graphics course at university. Think of it like a 1st-person shooter where you take a seed and plant it into the earth. The plant starts to grow and you will see it grow like in real life. Of course there are some environmental constraints that should be taken into account:
A. Time
B. (Sun)Light
C. Water
D. Other nutrition stuff like fertilizer

Don't bother about the technical aspects, i just want to know about the biological aspects of plant-growth. Let's assume we have a sunflower plant. As it starts to grow I get a couple of questions:
1. How fast does the plant stem grow according to a well defined amount of luminosity and water?
2. When do the first leaves develop?
3. How much thickness the stem gains per day/hour/minute?
4. What happens when suddenly there is less amount of luminosity and/or water? How the growth-rate will be affected?

These are only a few questions that arise when i think about this topic. Therefore i want to have a mathematical description of plant-growth under the environmental constraints mentioned above. I don't need a generic approach, but it would be nice to see such a formalism for e.g. a sunflower or Bellis Perennis. I also don't care about things that won't be able to see in the scene, like micro-biological-level - i just care about the whole architecture of the plant (stem, branches, leafes, fruits, (root)).

I did a lot of search on this topic including the computer modeling side: http://algorithmicbotany.org/papers/
https://www.informatik.uni-konstanz.de/en/deussen/publications/
But these sources focus more on techniques on how to generate images instead of the biological aspects.
Another book I've searched too solve my questions is "On Growth and Form" by Darcy Wentworth Thompson, but thats too general for my needs.

So are there any formal descriptions of plant-growth that take luminosity, water etc into account?

• not sure if anyone has specifically done this for plants, but I would guess that the answer is 'yes' - however, the detail that you seem to be interested may not be easily obtained from a simplified mathematical model. At least in growth of simple organisms (e.g. bacteria, fungi), models make a lot of assumptions on environment, growth conditions, etc - not sure how useful information is at the level of detail that you've described in your question. – Vance L Albaugh Oct 23 '16 at 15:13
• I'll add more detail here: I'm working on a prototype of a interactive computer simulation as a university project where you can place a seed of any kind of flower (lets assume Bellis perennis here because it's "simple" and well known). Now I have a sunlight in my scene and a watering can. After placing the seed I want to apply growth rules for the given kind of plant. So i want to know how the stem grows (height, thickness etc) and when and where leafs come up. So i need a formula for this specific plant which takes into account how much light, water and nutrition is given to the plant. – jackon Oct 23 '16 at 15:34
• I don't want to go down to the level of micro organisms like bacteria or cells because I'm aiming for visual representation only. So I'm just looking for a "approximated" mathematical representation of a given kind of plant. – jackon Oct 23 '16 at 15:38
• Yes it is possible and it is routinely done. For one example: team.inria.fr/virtualplants – Did Oct 23 '16 at 16:53
• @Did I've also found interesting sources right here: algorithmicbotany.org - I really don't want to read about technical aspects of how one could implement this in a computer application/software. The thing i need is something like "growth rules of plants for dummies" - I just want to read about the biological thing of how the growth of a specific plant behaves. Then you might say: Okay on an acre where the sun shines everyday the growth-rate per day is for example: 1cm * sunlight strength + randomness factor, after it has a height of x it develops leafs and the phyllotaxis is x+y*z – jackon Oct 23 '16 at 20:10