Spatial Slur

[ Design & Algorithms ]

Growing Dendrites

Since stumbling upon this paper by Ryo Kobayashi, I’ve been spending a shameful amount of time growing dendrites on my computer.

Isotropic dendritic growth

The process shown in the video above makes use of a phase field model to track an evolving interface between a supercooled liquid and a solid. While this seemed like unfamiliar territory at first, a quick look under the hood revealed a set of reaction-diffusion-like equations. The system is represented by two co-dependent scalar fields – one representing temperature and one representing the phase. The latter is either 0 (liquid) or 1 (solid) everywhere in the system except at the interface where it grades smoothly between the two extremes. At each step, the current temperature contributes to the change in phase and the change in phase contributes to the change in temperature. Over time, this feedback leads to instabilities in the interface which result in all the fancy branching patterns.

The Grasshopper definition is available here. Note that it uses the current release of SpatialSlur.dll which can be downloaded here.

d_02

Isotropic dendritic growth 1

a_04

Isotropic dendritic growth 2

b_03_2

Isotropic dendritic growth 3

b_04_2

Isotropic dendritic growth 4

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2 Comments

  1. Judi Lederman 2016.02.11

    These dendrites are gorgeous, (especially growth 4)and beg to be coloured! Very grateful for the instabilities in the interface.

    • Dave 2016.02.14 — Post author

      Thanks Judi – if I were less afraid of color, I’d try it myself.

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