The Algorithmic Beauty of Plants

(title taken from a wonderful book here)

Last year we ran a second year undergraduate computer practical in Biosciences introducing students to the ways in which computer simulations can be used to model plant growth. There are several neat scientific and practical ideas here. The students find that the diverse and complex range of beautiful plant forms can be mimicked by simulating simple, iterated rules (as in the pic). But the deeper idea is that these forms are not just mimicked by iterated rules – they genuinely emerge from such rules, not represented in a computer but in the biological language of the genome. This is the first time many students have met the idea that computational modelling allows a scientist to "play god" – they can make whatever changes they like to the rules and explore the effect on the simulated plants they grow. They also get to grips with algorithmic thinking – a highly transferrable skill given the expansion of coding and computational approaches across sectors.

Figure 1: L-Studio, simulating plant growth in computers from simple iterated rules. (top) An introductory exercise modelling a highly reduced model plant using a small number of growth rules. (bottom) A more involved simulation, based again around repeated application of simple rules, giving a fairly natural-looking plant structure.

The class is about 50 students, working in pairs or small groups with a computer. They are given some introductory exercises on “L-systems” (have a play e.g. here!), then given increasingly complicated structures to play with – including some famous fractals – and finally meet the translation to plant forms. In this way they learn to think algorithmically in a more abstract sense before the connection to biology is driven home. The exercises start fairly prescriptive, reproducing given structures. They then progress to a more investigative mode – given a particular plant form, how would you change its growth rules to, for example, outcompete tall neighbours, or disperse seeds more broadly? The final, exploratory, mode is the most interesting, where the students are given free rein, and design, adapt, and compare their own plant “designs”.

There are typically two members of staff and a handful of PhD students or postdocs acting in a TA capacity. We help with the initial setup – smoothing the way to this (unnatural for some) way of working with biological model systems in a computer. We then engage in a more scientific way with the groups, posing extension questions, guiding through questioning (careful not to just recite the solution to a given problem). In the final exploratory mode, we reduce the formality and jointly discuss scientific extensions and applications with the students and encourage the social aspect of the comparison and collaboration.

This class is an interesting one from a pedagogical point of view. The mode of learning shifts through the course of the two-hour session, from prescriptive to exploratory. Typically the class is very split in their uptake of this unfamiliar way of thinking. Some students love it, particularly the open-ended parts, and stick around to the end taking pictures of their plants and sending them to friends. Some frequently question the “point” of the class – a common question because logistics often mean they meet this class before lectures that naturally set up the modelling perspective. However, it usually just takes a few minutes of one-on-one discussion – illustrated with examples of our own research using computational modelling – to convince students of the utility both of the science and of the transferrable skill acquisition. One of my most personally rewarding experiences was with a student who started out almost aggressively sceptical about the point of these models – and whether the class would get him a better degree. After a discussion of the science and the transferrable value of computational modelling, he completely switched around and was interested in further pursuit of these topics. Other students are less polarised – they view the class as a box to be ticked. The final section of the class has an interesting influence here, where the enthusiasm of some groups rubs off onto the box-tickers. As such, there’s an interesting dynamic of teaching staff acting to catalyse the spread of enthusiasm – and of information – that emerges from the students’ own exploration.