I’ve got a huge interest in anthropic growth – namely growth enabled by humanity – and the rules behind its development. More importantly, we can now see a new materialist framework being contoured by philosophers like Manuel DeLanda together with Adrian Bejan and Constructal Theory, framework which encompasses both natural and anthropic growth and development under the same paradigm. The world is no longer split into Nature and Culture – Modernity’s dichotomy is being erased by rules and principles which guide both, making the distinction irrelevant.

Anyway, the main reason for this post is not to blabber about modernity and its dissolution (maybe that will come in the future in the writings section), but to share with you a processing implementation of RRT (Rapidly-exploring Random Trees) which is repurposed to grossly simulate growth through the perspective of Constructal Theory.

If you have a given surface (or volume) consisting of a population and the main goal of that population is to reach, or flow towards a specific point in the given surface, the most efficient structure, imposing the least flow resistance, is a dendritic one as shown in the video below.

In the case of a city (or the built environment), the main difference between it and a tree is that it does not have a single attractor, and flow is not linear in one direction. A city is composed of many attractors of different forces, each generating a different type of traffic flow which can be described as having different velocities, therefore requiring different flow resistances. For example, the average traveling speed in a medieval city was low, therefore the highly tortuous street network. As travel velocity increased, so the need for less flow resistance, which ultimately resulted in the Manhattan Grid. In this way you can differentiate between layers and layers of infrastructure. The video below shows how the networks of five different attractors merge with each other. Flow resistance is slowly decreased as the simulation progresses.

Finally, here’s a zipped processing sketch which contains a basic implementation of Constructal Theory generating infrastructure (based on this sketch). Of course, this can be enhanced further by limiting growth to certain angle variations and a host of other tricks which would more accurately simulate infrastructural growth. Each infrastructure type has different needs and limitations which can be transformed into parameters for this sketch.

You can play with an online version here!

Enjoy, and share alike. I am sharing out of goodwill, please do the same and do not abuse. Everything here is released under a Creative Commons Attribution-Noncommercial-Share Alike 3.0 Licence if not specified otherwise.

Here’s a movie of the thing in action (realtime):

Importing geometry (lines) from Rhino+GH into Processing, then switching back. Springs are rendered via a nifty hack, ie inverse proportional to the tension inside them. This corresponds to the most cluttered areas where particles get together more. The attraction force is good ‘ol newton’s law.

Of course, you can use it in 2d as well for any number of geometrical network relaxation uses you may find it useful for (street networks, for one, infrastructure at a more abstract scale, city planning, fancy urbanism projects, the like).

For the more architecturally inclined, here’s what happens when gravity enters the mix:

Nice, isn’t it? A nifty form-finding algorithm for a fancy support system of, well, any surface you please (I used a rectangle in example, a bit dull, but aren’t you fed up of double curvatures?). Here’s some screen grabs:

The structures presented here are self-normalizing, ie they reach an equilibrium at some point in the system. However, this is achieved via a delicate balance of quite a few parameters in the processing sketch: path resolution, spring strength and damping, world physics damping & min distance for the attraction force. I strongly recommend taking a look at traer’s physics lib documentation before starting to juggle the values (and to know where to look to juggle the values).

Enjoy & share alike!

For those who really like to play with voronoi regions and stuff, here’s the final grasshopper definition file (right click, save target as – else you’ll get a ~250kb of useless xml in your browser window).

The vcell component outputs now individual cells as closed polylines and closed nurbs curves. This is useful if you are using this for some urban project like i am i would have liked to, mostly due to easy offsetting and area calculation possiblities – included in the definition file – or height extrusion – included as well. You can even go further and color (using shaders) each cell coresponding with its mass/area/height etc.

Using processing to make a circulation study in a public area. It’s for the current school project. More details later.

I’ve used Shiffman‘s boids sketch as a start, and gradually started building up with some attractors, Point Obstacles (which are attractors with negative pull basically), and Linear Obstacles (which were a little bit tricky, but this helped out a lot). Also very inspirational were kokkugia‘s experiments.

When it’s nice and propper, I will  add some details and upload the code/sketch.