Hacked: The Mathematics of Leaf Vein Architecture
Researchers at the University of California - Los Angeles, have reverse engineered the mathematics behind the formation of leaf veins in growing and evolving plants across all species. The rules have been distilled into a simple, reproducible form which can be used by third parties to reliably shape new species.
Leaf veins are not the typical target of plant modelling in most VR systems, although they will certainly be of great interest to many microscale simulations. However, when you consider that leaf vein formation governs leaf shape formation, it is no great leap from there to use the recently discovered maths as part of the process for procedurally modelling new species for use as the vegetation elsewhere in a VR.
Most likely these equations will also form part of the foundations for algorithms to create whole plants mathematically and create new models that way.
The research, published May 15 in the journal Nature Communications, was intended for the study of global ecology and a method of allowing researchers to estimate original leaf sizes from just a fragment of a leaf. It is just a happy coincidence (as is so often the case) that this work has direct implications for virtual realities, and the creation of models to populate them. The intended initial hope for the work is that it will improve scientists' prediction and interpretation of climate in the deep past from leaf fossils.
Leaf veins are of tremendous importance in a plant's life, providing the nutrients
and water that leaves need to conduct photosynthesis and supporting them in
capturing sunlight. Leaf size is also of great importance for plants' adaptation
to their environment, with smaller leaves being found in drier, sunnier places.
UCLA graduate student Christine Scoffoni, three UCLA undergraduate researchers
and colleagues at other U.S. institutions measured hundreds of plant species
worldwide using computer tools to focus on high-resolution images of leaves
that were chemically treated and stained to allow sharp visualization of the
How Smaller Leaves Lead to Stronger Plants
Last year, Scoffoni and Sack proposed that small leaves tend to have their
major veins packed closely together, providing drought tolerance. That research,
published in the journal Plant Physiology, pointed to an advantage for improving
water transport during drought. To survive, leaves must open the stomatal pores
on their surfaces to capture carbon dioxide, but this causes water to evaporate
out of the leaves. The water must be replaced through the leaf veins, which
pull up water through the stem and root from the soil. This drives a tension
in the leaf vein "xylem pipes," and if the soil becomes too dry, air
can be sucked into the pipes, causing blockage.
The research also points to a new explanation for why leaf vein evolution allowed flowering plants to take over tens of millions of years ago from earlier evolved groups, such as cycads, conifers and ferns. Because, with few exceptions, only flowering plants have densely packed minor veins, and these allow a high photosynthetic rate — providing water to keep the leaf cells hydrated and nutrients to fuel photosynthesis — flowering plants can achieve much higher photosynthetic rates than earlier evolved groups, Sack said.
"While the major veins show close relationships with leaf size, becoming more spaced apart and larger in diameter in larger leaves, the minor veins are independent of leaf size and their numbers can be high in small leaves or large leaves," Sack said. "This uniquely gives flowering plants the ability to make large or small leaves with a wide range of photosynthetic rates. The ability of the flowering plants to achieve high minor-vein length per area across a wide range of leaf sizes allows them to adapt to a much wider range of habitats — from shade to sun, from wet to dry, from warm to cold — than any other plant group, helping them to become the dominant plants today."
The UCLA team explains that these patterns arise from the fact of a shared script or "program" for leaf expansion and the formation of leaf veins. The team reviewed the past 50 years of studies of isolated plant species and found striking commonalities across species in their leaf development. "Leaves develop in two stages," Sack said. "First, the tiny budding leaf expands slightly and slowly, and then it starts a distinct, rapid growth stage and expands to its final size."
Whilst this information is of course most pertinent to the plants of the physical
world, incorporating it into plant designs for virtual environments will have
the effect of greatly increasing believability and immersion, as the created
plants, following these natural 'rules' will match aspects of the plants from
wherever the user is from, increasing their tolerance for any strangeness in
your world. In the long, long term, once we have a more complete picture, it
may even help to enable plants following internal laws of physics and growth,
even outside specialised research
Why had these trends escaped notice until now?