The backflip of the simulated nauplius (Sage Jenson)

“…A World Dominated by Viscosity” (and other struggles)

Trouble Book Club
Sep 8, 2018 · 3 min read

simulation and art by Sage Jenson, writing by Kit Kuksenok

The nauplius — or, larval crustacean [1] — moves in one of three ways. Below, for example, is “swimming by vibration,” where the recovery stroke sends the nauplius backwards in what looks like an awkward and inefficient flailing:

From the supplementary materials for Borg, C. M. A., Bruno, E., & Kiørboe, T. (2012). The kinematics of swimming and relocation jumps in copepod nauplii. PloS one, 7(10), e47486. [2]

Although this “swimming by vibration” is indeed an unsatisfying way to get anywhere, it is actually neither “awkward” nor “inefficient.” Combining swimming and feeding, it involves “rotating feeding appendages at high frequencies” [1]. In this essay, we try to understand how the nauplius moves — by implementing our own simple model.

Another mode of movement, “swimming by jumping,” is subject of the scientific article [2] that we focus on today, and looks rather more graceful:

In the 2012 article by Borg, Bruno, & Kiørboe, scientists used this kind of footage to measure how far the legs of the nauplius got from its body, and in this way understand its motion.

In addition to reading and highlighting content in the article, Sage Jenson built amodel (or simulation) of nauplius propulsion. Below, the simulated nauplius starts out facing “backwards” and then flips, using the propulsion of its 20 legs, to face the right way:

The article served as a basis for implementing physics for legs that swim, and then modeling the movement of a creature with those legs. Above, each nauplius corresponds to a frame of movement.

If 20 legs sounds like too many legs then you’re right! It is, in fact.

An actual nauplius has 2 sets of 3 legs, and, in the model, it looks like this:

Half (above) and all (below) of the frames of the 6-legged nauplius model

As you can see, the simplified, triangular “body” looks little like the extravagant nauplius in reality. Models help us to understand a part of a complex system as abstracted from the rest of that system. In this case, focusing on propulsion, and implementing a model based on the paper [2], captures only some of the critical aspects of motion. In this example, the same back-flip motion is visible in both the 6-legged and the 20-legged case, but with only 6 legs the simulated motion is much more chaotic.

Without any resistance, or interaction with environment, the increasing the number of legs as a parameter is an effective, though unrealistic, way to provide more stability. To some extent, changing a parameter, like drag, on the legs is arguably including interaction with the environment. However, the paper this is all in spired by begins with the observation:

Copepod nauplii move in a world dominated by viscosity [2]

To capture the relevant aspects of how turbulent flow affects motion means including the medium in the model: the capacity for movement around the agent to also affect the agent.

The model was implemented in C++ using openFrameworks and the Box2D physics library. This essay is produced by Trouble Book Club, as part of a series on exploring the intersection of art and science. Featuring the simulation of artist Sage Jenson, summarized by Kit Kuksenok.

Bibliography: Further Reading & Inspiration

  1. Nauplius
  2. Borg, C. M. A., Bruno, E., & Kiørboe, T. (2012). The kinematics of swimming and relocation jumps in copepod nauplii. PloS one, 7(10), e47486. Accessed from

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