Perception of an ambiguous apparent motion is influenced by the immediately preceding motion. In positive priming, when an observer is primed with a slow-pace (1–3 Hz) sequence of motion frames depicting unidirectional drift (e.g., Right–Right–Right–Right), subsequent sequences of ambiguous frames are often perceived to continue moving in the primed direction (illusory Right–Right …). Furthermore, priming an observer with a slow-pace sequence of *rebounding* apparent motion frames that alternate between opponently coded motion directions (e.g., Right–Left–Right–Left) leads to an illusory continuation of the two-step rebounding sequence in subsequent random frames. Here, we show that even more arbitrary two-step motion sequences can be primed; in particular, two-step motion sequences that alternate between non-opponently coded directions (e.g., Up–Right–Up–Right; *staircase motion*) can be primed to be illusorily perceived in subsequent random frames. We found that staircase sequences, but not drifting or rebounding sequences, were primed more effectively with four priming frames compared with two priming frames, suggesting the importance of repeating the sequence element for priming arbitrary two-step motion sequences. Moreover, we compared the effectiveness of motion primes to that of symbolic primes (arrows) and found that motion primes were significantly more effective at producing prime-consistent responses. Although it has been proposed that excitatory and rivalry-like mechanisms account for drifting and rebounding motion priming, current motion processing models cannot account for our observed priming of staircase motion. We argue that higher order processes involving the recruitment and interaction of both attention and visual working memory are required to account for the type of two-step motion priming reported here.

*motion aftereffect*(Hiris & Blake, 1992; Anstis, Verstraten, & Mather, 1998; Glasser, Tsui, Pack, & Tadin, 2011) and is also referred to as

*negative motion priming*. More recently, researchers have shown that, if the static image is replaced with a sequence of ambiguous frames (such as flickering counterphase sine wave gratings), a stronger and longer lasting negative priming effect can be induced (Bex, Verstraten, & Mareschal, 1996; Nishida & Ashida, 2000). In such studies, participants are primed with a sequence of frames depicting unambiguous unidirectional motion (e.g., Right–Right–Right–Right) and then report that a sequence of subsequently viewed ambiguous frames, which can be resolved in one of two mutually exclusive directions, contains motion traveling opposite the primed direction (e.g., Left–Left–Left–Left). The basis of this reversal is believed to result from opponent coding observed in motion-sensitive neurons and constitutes a form of adaptation (Simoncelli & Heeger, 1998; Huk, Ress, & Heeger, 2001).

*visual inertia*(Anstis & Ramachandran, 1987),

*visual motion priming*(Pinkus & Pantle, 1997), and most recently

*positive priming*(Takeuchi, Tuladhar, & Yoshimoto, 2011; Yoshimoto, Uchida-Ota, & Takeuchi, 2014), and it can bias the perception of subsequent ambiguous frames to be moving in the

*same*direction as the priming frames. Specific stimulus parameters determine whether the induced illusory motion will be judged positive or negative relative to the priming frames. Such factors include prime duration, prime velocity, frame rate, length of the interstimulus interval (between the offset of priming frames and the onset of testing frames), and stimulus contrast (Kanai & Verstraten, 2005; Takeuchi et al., 2011; Yoshimoto et al., 2014; Heller & Davidenko, 2018).

*maximally ambiguous multistable*stimuli, we present novel evidence that positive priming can operate over more complex spatiotemporal motion sequences—in particular, two-step, staircase-like motion sequences (e.g., Up–Right–Up–Right). Here, we show that such staircase motion sequences can be primed similarly to simpler drifting (e.g., Up–Up–Up–Up) or rebounding (e.g., Up–Down–Up–Down) motion sequences (Davidenko, Heller, Cheong, & Smith, 2017; Davidenko & Heller, 2018). Furthermore, we demonstrate that priming arbitrary two-step sequences is far more effective when the priming motion contains at least one repetition (i.e., two instances) of the sequence. Finally, we show that primes containing visual motion signals are more effective than symbolic primes (i.e., arrows). Our results suggest that visual working memory and selective attention must work together to produce the subsequent complex illusory percepts.

*rebounding bias*(Davidenko et al., 2017; Davidenko & Heller, 2018). A one-way repeated-measures analysis of variance (ANOVA) on the collapsed distribution of responses (excluding the combined denoting responses that included at least one Other button press responses) confirmed that the proportion of responses varied significantly by motion direction,

*F*(15, 367) = 8.74,

*p*< 0.0001. Figure 2B (bottom) shows this response distribution broken down by the preceding priming motion. The two top rows show the distribution of responses following drift primes, the next two rows following rebound primes, and the last two rows following staircase primes, as indicated by the arrows along the

*y*-axis.

*F*(15, 2207) = 8.41,

*p*< 0.0001, and a significant interaction between primed direction and reported direction,

*F*(75, 2007) = 7.14,

*p*< 0.0001. The main effect of reported direction reflects an overall propensity to report rebounding motion over other types of motion. Critically, the interaction indicates that the directions reported varied significantly as a function of the priming directions.

*t*-tests comparing the response rate for prime-consistent responses versus prime-inconsistent responses of the same type. Figure 3A shows the distribution of drift responses following drift primes. Note that the most frequent drift responses following drift primes matched the direction of the priming motion. Figure 3B directly compares the average proportion of prime-consistent (

*M*= 0.242) and prime-inconsistent (

*M*= 0.053) drift responses following drift primes. A paired

*t*-test confirmed that prime-consistent responses were significantly more frequent,

*t*(22) = 2.75;

*p*= 0.005, one-tailed; Cohen's

*d*= 0.57.

*M*= 0.314) and prime-inconsistent (

*M*= 0.170) rebound responses following rebound primes, revealing a significantly larger proportion of prime-consistent responses, paired

*t*(22) = 2.75;

*p*= 0.04, one-tailed; Cohen's

*d*= 0.37.

*M*= 0.251) was significantly larger than prime-inconsistent staircase responses following staircase primes,

*M*= 0.048; paired

*t*(22) = 3.22;

*p*= 0.004, one-tailed; Cohen's

*d*= 0.67. This constitutes evidence that two-step (i.e., staircase) motion sequences can be primed.

*p*< 0.05) was 0.1217. According to this criterion, all participants performed well above chance, with the lowest performance being 0.250 and the highest 1.00, with a mean of 0.750. Similar catch trial performance was observed in Experiments 2, 3, and 4, so we do not report the details of catch trial performance for those analyses.

*M*= 0.231) occurred nearly as frequently as Up–Right responses (

*M*= 0.236) following Up–Right–Up–Right primes. Because of the block design, it is difficult to distinguish whether these responses were directly primed by the preceding motion, or whether they were primed in a more global way as a result of seeing many such motion sequences across the experimental block. For example, during a staircase block, where every trial started with a staircase sequence (either Up–Right–Up–Right or Down–Left–Down–Left), participants may have formed an expectation that those specific staircase sequences are frequent and to be expected, and it was this global expectation that influenced what they perceived and reported during the test frames.

*d*in the staircase condition was 0.67), a power analysis with 80% power to detect an effect size of 0.33 with an alpha level of 0.05 would require a sample of about 67 participants. We recruited 68 undergraduate students (51 identifying as female, 15 as male; mean age, 20.1 years; range, 19–25) from UCSC, who gave informed consent and participated in exchange for course credit. The study was approved by UCSC's Institutional Review Board and took approximately 25 minutes to complete.

*F*(15, 1087) = 20.35,

*p*< 0.0001. Figure 4B shows this broken down by the 16 different motion prime conditions (the first four rows show drift primes, the next four rebound primes, and the next eight staircase primes). Darker blue colors on the matrix indicate more frequent responses. As can be seen, the diagonal elements representing prime-consistent responses have a darker blue color, indicating that prime-consistent motion sequences were frequently reported.

*F*(15, 17,407) = 5.74,

*p*< 0.0001; a significant main effect of reported direction,

*F*(15, 17,407) = 15.9,

*p*< 0.0001; and a significant interaction,

*F*(225, 17,407) = 10.5,

*p*< 0.0001. The main effect of reported direction reflects an overall propensity to report rebounding motion over other types of motion. Critically, the interaction indicates that the directions reported varied as a function of the priming directions.

*t*-tests comparing the frequency of prime-consistent responses versus prime-inconsistent responses of the same motion type. Figure 5A shows the distribution of drift responses following drift primes. The diagonal elements (which indicate prime-consistent responses) have a darker blue color than the rest of the cells. To quantify this, Figure 5B compares the average proportion of prime-consistent (

*M*= 0.112) and prime-inconsistent (

*M*= 0.019) drift responses following drift primes, showing a significantly larger proportion of prime-consistent responses, paired

*t*(67) = 6.35;

*p*< 0.0001, one-tailed; Cohen's

*d*= 0.77. Similarly, Figure 5C shows the distribution of rebound responses following rebound primes. Figure 5D compares the average proportion of prime-consistent (

*M*= 0.179) and prime-inconsistent (

*M*= 0.075) rebound responses following rebound primes, revealing a significantly larger proportion of prime-consistent responses, paired

*t*(67) = 5.38;

*p*< 0.0001, one-tailed; Cohen's

*d*= 0.65.

*M*= 0.132) was significantly larger than that for prime-inconsistent staircase responses (

*M*= 0.024), paired

*t*(67) = 7.83;

*p*< 0.0001, one-tailed; Cohen's

*d*= 0.950. This again shows that arbitrary two-step motion sequences can be primed similarly to drifting and rebounding motion sequences.

*F*(15, 1055) = 12.85,

*p*< 0.0001. Figure 6B shows this distribution broken down by the 16 different motion prime conditions (the first four rows show drift primes, the next four show rebound primes, and the next eight show staircase primes. Darker blue colors indicate more frequent responses. As can be seen, the diagonal elements representing prime-consistent responses have a darker blue color for drift and rebound motion primes, but this is not as clear for staircase primes.

*F*(15, 16,895) = 14.26,

*p*< 0.0001; and a significant interaction between primed direction and reported direction,

*F*(225, 16,895) = 8.84,

*p*< 0.0001. The main effect of reported direction reflects an overall propensity to report rebounding motion over other types of motion. Critically, the interaction indicates that the directions reported varied significantly as a function of the priming motion.

*t*-tests comparing the frequency of prime-consistent responses versus prime-inconsistent responses of the same type. Figure 7A shows the distribution of drift responses following drift primes. The diagonal elements (which indicate prime-consistent responses) have a darker blue color than the rest of the cells. To quantify this, Figure 7B compares the average proportion of prime-consistent (

*M*= 0.126) and prime-inconsistent (

*M*= 0.022) drift responses following drift primes, showing a significantly larger proportion of prime-consistent responses, paired

*t*(65) = 5.08;

*p*< 0.0001, one-tailed; Cohen's

*d*= 0.63. Similarly, Figure 7C shows the distribution of rebound responses following rebound primes. Figure 7D compares the average proportion of prime-consistent (

*M*= 0.155) and prime-inconsistent (

*M*= 0.067) rebound responses following rebound primes, revealing a significantly larger proportion of prime-consistent responses, paired

*t*(65) = 5.08,

*p*< 0.0001, one-tailed; Cohen's

*d*= 0.59.

*M*= 0.047) was significantly larger than prime-inconsistent staircase responses (

*M*= 0.024),

*t*(65) = 2.87;

*p*= 0.006, one-tailed; Cohen's

*d*= 0.35. Although this result suggests that it is possible to prime a staircase sequence with only two priming frames, the effect size and overall proportion of staircase-consistent responses were small.

*F*(15, 16,895) = 14.26,

*p*< 0.0001, reflecting that rebound motion responses occurred more frequently than other types of responses. Critically, there was also a significant interaction between the number of priming frames and the motion type, such that prime-consistent staircase responses were significantly more frequent following four-frame primes (

*M*= 0.1321) compared with two-frame primes (

*M*= 0.047). A followup two-sample

*t*-test confirmed that this difference was significant,

*t*(132) = 5.16;

*p*< 0.0001, one-tailed; Cohen's

*d*= 0.89.

*F*(15, 34,303) = 30.90, indicating a rebound bias and a significant main effect of prime type,

*F*(1, 34,303 = 11.55,

*p*= 0.001, indicating significantly more cardinal direction motion responses following arrow primes. There was also a significant two-way interaction between prime direction and reported direction,

*F*(225, 34,303) = 11.09,

*p*< 0.0001, indicating that the primed direction affected the reported direction. Critically, there was a significant three-way interaction among primed direction, reported direction, and prime type,

*F*(225, 34,303) = 2.64,

*p*< 0.0001. The three-way interaction indicated that motion primes were more effective than arrow primes at influencing the distribution of reported directions (see also Figure 12).

*t*-tests comparing the response rate for prime-consistent responses versus prime-inconsistent responses of the same type, separately for the motion prime block (Figure 10) and the arrow prime block (Figure 11). Figure 10A shows the distribution of drift responses following drift motion primes. The diagonal elements (which indicate prime-consistent responses) have a darker blue color than the other cells. To quantify this, Figure 10B compares the average proportion of prime-consistent (

*M*= 0.092) and prime-inconsistent (

*M*= 0.012) drift responses following drift primes, showing a significantly larger proportion of prime-consistent responses, paired

*t*(66) = 4.61;

*p*< 0.0001, one-tailed; Cohen's

*d*= 0.56. Similarly, Figure 10C shows the distribution of rebound responses following rebound primes in the motion prime block. Figure 10D compares the average proportion of prime-consistent (

*M*= 0.2355) and prime-inconsistent (

*M*= 0.090) rebound responses following rebound primes, revealing a significantly larger proportion of prime-consistent responses, paired

*t*(66) = 5.61;

*p*< 0.0001, one-tailed; Cohen's

*d*= 0.69. Figures 10E and 10F show results for staircase primes. The average proportion of prime-consistent staircase responses (

*M*= 0.117) was significantly larger than prime-inconsistent staircase responses (

*M*= 0.025), paired

*t*(65) = 6.37;

*p*< 0.0001, one-tailed; Cohen's

*d*= 0.78. Overall, the results of the motion priming block constitute a successful replication of Experiment 2, indicating that four frames of apparent motion are sufficient to prime drift, rebound, and staircase motion sequences.

*M*= 0.042) and prime-inconsistent (

*M*= 0.021) drift responses following drift primes, showing a significantly larger proportion of prime-consistent responses, paired

*t*(66) = 4.05;

*p*= 0.0001, one-tailed; Cohen's

*d*= 0.49. Similarly, Figure 11C shows the distribution of rebound responses following rebound primes in the arrow prime block. Figure 11D compares the average proportion of prime-consistent (

*M*= 0.171) and prime-inconsistent (

*M*= 0.100) rebound responses following rebound primes, revealing a significantly larger proportion of prime-consistent responses, paired

*t*(66) = 5.85;

*p*< 0.0001, one-tailed; Cohen's

*d*= 0.71. Figures 11E and 11F show results for staircase primes. The average proportion of prime-consistent staircase responses (

*M*= 0.065), although small, was significantly larger than prime-inconsistent staircase responses (

*M*= 0.028), paired

*t*(66) = 5.66;

*p*< 0.0001, one-tailed; Cohen's

*d*= 0.69. These results show that four frames of symbolic primes (i.e., arrows) are sufficient to prime drift, rebound, and staircase motion sequences.

*F*(1, 401) = 12.03,

*p*= 0.0009, and a significant main effect of primed direction,

*F*(2, 401) = 54.70,

*p*< 0.0001, but no significant interaction,

*F*(2, 401) = 0.35,

*p*> 0.5. The main effect of prime type indicated overall more prime-consistent responses during the motion prime block compared with the arrow prime block, and the main effect of primed direction reflects the rebounding bias. Overall, motion primes were significantly more effective at priming motion than arrow primes, and this benefit did not vary as a function of motion type (drift, rebound, or staircase).

*repeating sequence*(e.g., Up–Right followed by another instance of Up–Right), then the motion sequence is well defined and can be reinstantiated during subsequent ambiguous frames. Therefore, the property of repetition seems to matter in the degree to which a motion sequence can be primed.

*-*opponent directions, such as Up and Right, or more generally between any arbitrary pair of motion directions. In order for the system to predict Up motion on a given frame transition following Up–Right–Up–Right motion, the system would have to “remember” that the motion direction two steps earlier was Up. This additional processing layer would therefore rely on sequence learning mechanisms and is likely to reside in higher order cortical regions where visual working memory can maintain these spatiotemporal motion patterns across multiple frame transitions. Such high-order sequence learning mechanisms have been previously proposed to account for serial order effects in other aspects of learning, as well as in the encoding and physical reproduction of ordered motion sequences (Lewandowsky & Murdock, 1989; Agam, Bullock, & Sekuler, 2005). Future models of motion priming will thus need to consider the role of visual working memory and sequence learning in addition to feature-based selective attention.

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