Wenderoth, Bock & Krohn (2002)

|Review| Learning a new bimanual coordination pattern is influenced by existing attractors.

In the last post, we looked at an investigation by Fontaine and authors into a prediction made by the Dynamic Pattern Approach (DPA) that learning a new coordinated rhythmic movement is harder near stronger attractors (Zanone & Kelso, 1994). They found quite the opposite: Learning was easier near the stronger attractor, not harder.

In an attempt to investigate this further Wenderoth and authors led out two questions:

  1. Does the distance between existing attractors and the to-be-learned pattern influence the learning process?
  2. Is a new phase relationship close to the 0° attractor learned in a different way than one close to the 180° attractor?

With the DPA coming under scrutiny from the Fontaine results, the authors made the sensible choice to sit on the fence and make no predictions.  They simply ask the questions. That said, even with the confidence in this approach somewhat knocked, we can tell by the language of these questions just how dominant the DPA was during this time in the CRM literature. Both questions are framed within the realm of the attractors, taking their existence as veritas irrefutabilis.

But is it? If this study also contradicts the predictions made by the DPA, ought we to question the existence of such attractors thus, the very basis of the approach?

Putting it to the test

The methodology used to investigate these questions was to divide participants into 1 of 5 different groups dependent on ɸ. Those were: 36°, 60°, 90°, 120° and 144°. Each participant completed 35 trials in which their task was to produce their to-be-learned phase as accurately as possible. Each trial consisted of 30s of tracking a target (at the to-be-learned phase) using lissajous feedback, followed by 30s of producing the to-be-learned phase without any feedback. All movements were produced bimanually.


Like the Fontaine experiments, the variables of interest were stability and accuracy.

Stability increased irrespective of the to-be-learned pattern. There were no significant main or interaction effects.  In other words, the proximity of the to-be-learned pattern to the 0° and 180° attractors didn’t make any difference whatsoever. This mirrors the later practice Fontaine results.

Again, much like the Fontaine results, accuracy painted a slightly more complex picture. Initially, 90° and 60° were produced with substantially larger errors than other groups (90° having even larger error rates than 60°). Final accuracy was dependent on the ɸ group, this was confirmed with a significant trial main effect and a group by trial interaction. 36° was produced with the highest accuracy. 60° was produced with the lowest accuracy.


In an attempt to look at a pre vs post (see Figure 1): Authors performed a mean absolute phase error (accuracy) across trials 1-5 and trials 31-35 for each group. For each FB condition, a separate ANOVA with the between factor GROUP (the 5 RPs) and the within factor TRIAL (Initial, Final) was performed.

Wenderoth PRE-POST noFB EDIT

Figure 1. Adapted from Wenderoth, Bock & Krohn (2002): Mean and standard error of accuracy averages for each group across trials 1-5 (shaded) and trials 31-35 (clear) for the “No Feedback” condition.

Initially (trials 1-5) patterns close to attractors (36° and 144°) were performed with higher accuracy than other patterns, presenting the typical inverted U HKB pattern. This in itself is unusual if the DPA were to be correct. 36° and 144° seem to benefit from a close proximity to the 0° and 180° attractors rather than seeing the predicted inhibition effect.

In the final 5 trials, this pattern no longer holds. 36°, 60° and 90° showed large improvements and patterns close to 0° were produced with higher accuracy than those close to 180°. Another result of note were the large phase errors of the groups closest to the 180° attractors. These were 39.2° for the 120° group and 31.72° for the 144° group. Interestingly, the error rate doesn’t increase in proximity to 180° but in proximity to 90°.


Mirroring Fontaine et al., patterns close to 0° were produced with higher accuracy than those close to 180°. Can we explain these results in the context of attractors? Might 180° be a stronger attractor than 0°? Thus be the reason for this result? In short, no. If that were the case increasing the frequency of 0° would result in a transition to 180°. The opposite is true. Increasing the frequency of 180° results in a transition to 0°.

Might there be other stabilising mechanisms involved when learning a new pattern that perturbs the attractor layout? Wenderoth et al (2002) suggest that the 180° attractor was additionally stabilised by other mechanisms (e.g. by involuntary trunk movements). They assume that the trunk moves more for anti-phase than in-phase, thus having a postural stabilising effect. That said, they state that no differences in trunk movements were observed (though I don’t believe they were measured empirically). They go on to state that postural adjustments may have differed between groups, but they were probably too small to matter.

This is no more an explanation than a hand rubbing a chin accompanied with a ‘hmmm’. They make a suggestion as to why, only to say directly after it, ‘but maybe not, we don’t really know’.

At this point, we must place the veritas irrefutabilis status of the attractors in a sceptical light. We have attempted to explain the above result in terms of the attractor landscape with little success. Perhaps the easiest way to explain this result is to say, there are no attractors.

But from here, where do we go?

Something is driving a specific pattern of results: 0° is more stable than 180° and patterns closer to 0° are easier to learn than those close to 180°. If this isn’t driven by attractors, then what?


Alternate theories that attempt to explain the above pattern of results.

End note: Two separate lines of inquiry

  1. Wenderoth and authors suggest a separate mechanism is used by the CNS to produce unknown phases of CRM, named Rhythm Setting. This idea was tested under this very paradigm. Read more about Rhythm Setting here.
  2. Having all participants tested under both lissajous feedback and no feedback, the authors were interested in the difference between the feedback conditions and if any transfer would occur. This inquiry will be discussed in a separate post.


Fontaine, R. J., Lee, T. D., & Swinnen, S. P. (1997). Learning a new bimanual coordination pattern: reciprocal influences of intrinsic and to-be-learned patterns.Canadian Journal of Experimental Psychology = Revue Canadienne de Psychologie Expérimentale51(1), 1–9. Retrieved from http://www.ncbi.nlm.nih.gov/pubmed/9206321

Zanone, P.G., & Kelso, J.A.S. (1994). The coordination dynamics of learning: Theoretical structure and experimental agenda. In S.P. Swinnen, H. Heuer, J. Massion, & P. Casaer (Eds.), Interlimb coordination: Neural, dynamical, and cognitive constraints (pp. 461-490). San Diego, CA: Academic Press.

Wenderoth, N., Bock, O., & Krohn, R. (2002). Learning a new bimanual coordination pattern is influenced by existing attractors. Motor Control, 6, 166–182.





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