Ceci n’est pas un arbre

To abstract the real world –  to “move away from the concrete world and move towards ideas and concepts” (Khan Academy lecture of “Abstract”) – is a skill shared by both artists and scientist. It is neatly illustrated in the process of abstracting trees for modelling satellite observations.

In the science of remote sensing of forests we often have to build some kind of physical model for simulating the observations.  Since we don’t want to replicate real trees in their entirety, which would be unnecessarily complex, we simplify the forest so that we capture the essence of what makes a tree, a tree (within the realms of any particular observation technique). It often results in abstract, symbolic representations of trees and forests, and in this way shares many of the same goals as visual artists: to capture the essence of their subject rather than to simply replicate its appearance.

To misquote Picasso  (with my changes in square brackets): “Drawing is no joke. There is something very serious and mysterious about the fact that one can represent a living [tree] with line alone and create not only [its] likeness but, in addition, an image of [what it] really is. That’s the marvel!”

So this post is a fun look at some representations, visualisations and abstractions of trees, from both artists and remote sensing scientists.

  Matisse, Study of Trees.  It’s a regular branch structure and equal sized leaves. Note how he gets the tapering right in the branches, but not in the trunk (at least the one of the left). http://www.henri-matisse.net/drawings/du.html
  Hammond and Niklas at Cornell University have been developing a growth model, SERA. Trees are light absorbers, hungry for as much light as they can find. They are only crowns and trunks.  (Hammond and Niklas, 2009). Matthew Brolly and I used this model recently for simulating radar images of forests.
  Matisse has no individual leaves this time, but only crowns, trunks and one or two major branches. (http://gladsdotter.wordpress.com/tag/matisse/)
  In forest mapping in Australia Lucas, et al, created a box model to try to capture the heterogeneity of the landscape so they could model the radar backscatter (Lucas et al, 2006). Crowns become boxes, trunks still included.
  Less abstraction, more as focus, Klimt details the trunks of the forest and ignores the canopy (Forest of beech trees c1903).
  Matthew Brolly and I wanted to focus on the trunks too with our Matchstick Model. This was because long wavelength microwaves don’t interact with the forest canopy very much (http://www.sciencedirect.com/science/ ).
  Mondrian’s Apple Tree in Blossom (www.eecs.berkeley.edu/~bh/ssch18/trees.html) captures both the complexity and rhythm of the tree.
  My first experience with abstraction of trees was when I worked with Dirk Hoekman in Wageningen (Woodhouse and Hoekman, 2000). Here we used a common layering approach, where the forest canopy is composed of cylinders.
  Seurat in la Grande Jatte, (1884) captures the random, but smooth, nature of a tree crown. Again, a simplistic “crown plus trunk” approach is used.
  Couteron, et al, take a lollipop approach (www.earthzine.org/2012/04/23/) which is very common when modelling the visible and near infrared imagery.  The crowns are composed of random points of reflection, much like Seurat.
  Paul Klee’s Fig Tree draws out the clumping of a tree crown.
  Suarez et al 2008  also look at random clouds of scattering particles in regular crown shapes.
  David Hockney’s Bigger Trees is only fully appreciated at full scale, but it is a fine representation of the architecture of deciduous trees. Note, no leaves.
  In 2006 I did some modelling using a macroecology model (Woodhouse, 2006). Simple, stylised architecture. Large components, small components, angles. No leaves.
  Mondrian,Composition Trees II  is getting very abstract. Large components, small components, angles. But the form is still there.
  Lacaze and Roujean, 2001  use a model with layered canopy and vertical stems. Homogenous, random scatterers within the crowns.


  1. This is really great! It is interesting to see so many different representations of trees. I could add a few lidar trees to that 🙂

  2. This one is good – Hockney is clearly a ‘green goo’ modeller at heart, as the leaves are not even connected to the stems.

    1. Thanks for the link. 🙂
      The NPR article isn’t quite correct, though, to say that no-one has an answer for preservation of the cross sectional area as noted by da Vinci. The simple “pipe model” explains it. Namely that the majority of the functional structure of tree branches is pipework that either takes water and nutrients from roots to leaves, or sugars from leaves to roots. If you imagine a holding a bunch of straws then diverging them at the top into branch structures, then you can imagine why the total cross sectional area of the daughter branches (approximately) equals the cross sectional area of the parent. I say approximately, as it is not the same for all trees. See the many papers by West, Brown and Enquist in Nature and Science for details.

  3. Very fascinating! I love the intersection of art and science. Beautiful job of matching the two worlds up, by the way. This whole thing reminds me of the fable of the blind men and the elephant. What is a tree like… a box, an umbrella, a matchstick…

    I found your post through TreeMagazine and will reblog again.

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