Movement direction is given in radians (ranging from 0 to 2
π rad; 0 = vertical down), and speed in degrees of visual angle per second or °/s. Parameters
σ1,
σ2,
η,
μ, Wa, and Ws are time series. Parameter
β ranged from 0 to 1, was constant during one stimulus, and was the key independent variable in the experiment. The variables
σ1 and
σ2 were sine waves with frequencies of 0.3 Hz and 0.57 Hz, respectively. Gaussian was
η noise (mean 0, SD 2.77 rad) smoothed using a moving average over 0.5 s.
μ was 5.9°/s. W, composed of Wa (movement angle) and Ws (speed), stands for bursts of wind. It was used to evoke the impression of an external force acting on the moving object. Ws consisted in linearly increasing acceleration for 0.17 s up to 11.8°/s, then linearly increasing deceleration (at one tenth of the intensity of acceleration) for 0.17 s, then constant deceleration until prewind speed for 0.72 s. Wa, the direction of the wind, was random within a window of ±1.05 rad from vertical up. Bursts of wind occurred seven times at random intervals during the animation and could be overlapping in time. The speed time-series were normalized to the range of 2.95°/s to 10.33°/s. Coordinates were calculated by projecting speed magnitude values on
x- and
y-axes according to the speed angle values, then integrating over time. All computations were implemented in pixels/frame, and final coordinates were rounded to the nearest integer. There was no intended or observed systematic relation between the speed of the dot and the curvature of its trajectory (two-thirds power law; see Viviani & Stucchi,
1992). We aimed to keep as many low-level characteristics of the stimuli as similar as possible, but some changes were necessary: vertical positions on the screen, mean acceleration, movement directions, and overall aspect of the trajectory were very similar, while horizontal positions and the profile of speed and acceleration changed (see more detailed analysis in
Experiment 2). Stimuli were created and displayed using MATLAB R2010A (The MathWorks, Natick, MA) with the Psychtoolbox extensions (Brainard,
1997; Kleiner, Brainard, & Pelli,
2007; Pelli,
1997).