Economy and anticipation in graphic stroke sequences *

Human Movement Science 11 (1992) 71-82

North-Holland

71

Economy and anticipation in graphic stroke sequences *

Arnold J.W.M. Thomassen, Ruud G.J. Meulenbroek and Marion P.E. Hoofs NICI, lJnir:ersity of Nijmegen, Nijmegen, The Netherlands

Abstract

Thomassen, A.J.W.M., R.G.J. Meulenbroek and M.P.E. Hoofs, 1992. Economy and anticipation

in graphic stroke sequences. Human Movement Science 11, 71-82.

The selection of stroke sequences in graphic production is studied, focussing on planning and

anticipation of economy. An experiment is presented in which fifteen subjects copied 256

variations of a geometrical four-segment pattern characterized by parallel lines. The stroke

sequences adopted by the subjects are shown to depend on a number of constraints including the

execution of the parallel segments in immediate succession and in the same direction, and the

performance of the final stroke in a preferred direction. Although they are often effective only at

subsequent stages in performance, these constraints appear to determine the entire organization

of a large proportion of the stroke sequences. Thus, the planning of graphic action involves the

anticipation of economy later in the sequence. It is speculated that such anticipation may be a

feature of complex-movement organization in general.

A major aspect of sequencing in movement involves the selection of the successive segments in complex action sequences. This aspect has received only very limited attention in movement research. One area in which the planning and execution of such sequences can be studied fruitfully is the domain of graphic action. From an often immense

* The present research was supported by the Netherlands Organization for Scientific Research

(NWO), Project 560-259-035, and by the European Strategic Programme for Research and Development in Information Technology (ESPRIT), Project 419. The paper was written whilst

the first author was a Fellow at the Netherlands Institute for Advanced Study (NIAS), Wassenaar.

Requests for reprints should be sent to A.J.W.M. Thomassen, Nijmegen Institute for Cogni-

tion Research and Information Technology (NICII, University of Nijmegen, P.O. Box 9104, 6500 HE Nijmegen, The Netherlands.

0167-9457/92/$05.00 0 1992 - El sevier Science Publishers B.V. All rights reserved

72 A.J. W.M. Thomassen et al. / Graphic stroke sequences

number of possibilities, the drawing subject selects one stroke sequence that will lead to the intended graphic representation. He or she does so under a number of constraints, ranging from biomechanical to cultural ones. Especially in the case of copying meaningless geometrical patterns, the subject has to make ad hoc decisions, relying on implicit knowledge of the motor system. Such patterns have indeed been used over the past two decades (Goodnow and Levine 1973; Ninio and Lieblich 1976; Simner 1981; Thomassen and Teulings 1979; Van Sommers 1984). These studies have revealed the operation of a set of principles or rules for-which the collective term grammar of action has been introduced (Goodnow and Levine 1973). The rules are concerned with starting points (start at the left extreme; start at the top), with stroke directions (draw downwards; draw rightwards), and with stroke sequences (continue without pen lifts; anchor later strokes to earlier ones; complete parallels in immediate succession).

In our previous studies we have shown that adherence to these rules is sensitive to the context in which the patterns are presented (Thomassen et al. 19891, and that for a given set of patterns the rules can be quantified and their operation modelled by a simulation programme (Thomassen and Tibosch 1991). Moreover, we showed that the operation of graphic-production rules is reflected by latencies and kinematics (Thomassen et al. 1991). These studies concentrated on the selection and execution of individual strokes without paying attention to planning and anticipation. The latter aspects will be studied in the present experiment. We concentrate on the repeated use of the same motor program. To this end, the patterns used in the experiment have two parallel lines. Apart from some other manipula- tions, the patterns have eight different orientations so that structural effects due to the shape of the model pattern can be distinguished from biomechanical effects involved in the orientation of the pattern in relation to the arm-hand effector system and its associated stroke- direction preferences (Meulenbroek and Thomassen 1990, 19911.

Our earlier study (Thomassen and Tibosch 1991) demonstrated a strong tendency to start a later, separate stroke from a point on an earlier one (anchoring); this tendency was shown to be associated with precision (Thomassen et al. 1991). An even stronger tendency appeared to involve connecting subsequent strokes by keeping the pen on the writing surface (threading), i.e., to continue pen-down across angles. This strategy is presumably followed because it permits unin-

A.J. U! M. Thomassen et al. / Graphic stroke sequences 73

terrupted tactile and visual feedback about the trace, and makes the attention-demanding repositioning of the pen on paper unnecessary. These tendencies operate as two dominant constraints in copying. The economic advantage of making repeated use of the same motor program (Rosenbaum et al. 1986) may introduce a third tendency, namely that of producing identical or similar strokes in immediate succession. A final issue is whether there is a tendency to end graphic sequences in a relaxed biomechanical state, as observed in other domains of manual performance (Rosenbaum and Jorgensen 1992). To address these issues, we investigate the effect of the patterns’ structure and orientation on the selection of the stroke sequences by which they are copied.

Method

Subjects and materials

Fifteen naive, right-handed students participated in the experiment. The basic stimulus pattern was composed of four straight segments ’ (see fig. 1). The th ree main variations applied factorially to the basic pattern involve (1) two Mirror Images; (2) two Parallel Forms ( 156 1

parallel either to I12 I or to 134)); and (3) eight Orientations of the entire pattern (extreme (2) of I23 I being oriented at 0, 45, 90, 135, 180, 225, 270, 315 degrees). Two other variations were of a metric kind; they will not be discussed here. * The variations resulted in 256 different patterns, which were presented once in a random order.

Apparatus and procedure

The copying task was performed with a pressure-sensitive pen on a digitizer (Calcomp 9000), connected to a VAX workstation (for tech-

’ Segments of the stimulus patterns are denoted by two digits in between vertical bars, e.g., 112 1, to indicate their directionless nature. Strokes or stroke sequences are performance units; these

are denoted by a series of digits, e.g., 12 or 1234, 65, to indicate the actual direction of the

stroke(s) and the order of the sequence, possibly interrupted by a pen lift, as denoted by a comma. Angles are denoted by ( ).

* The metric stimulus variations involved (a) two positions of join (5) and (b) four size

combinations of the lengths of I12 1, 134 / and 156 I (see fig. 1). The effects of these variations were small. In this study, the data are pooled across the eight conditions involving variations (a) and (b).

74 A.J. WM. Thomassen et al. / Graphic stroke sequences

nical details, see Teulings and Maarse 1984). The data were seg- mented interactively into four pen-down strokes having one of eight movement directions (classified according to those of the stimulus orientations), separated by low-velocity changes in direction and, where observed, by pauses and pen lifts. Prior to the 256 experimental patterns, 32 simpler patterns were copied for practice. Patterns were presented on the response sheets in rows of eight boxes of 20 x 20 mm. Each pattern was to be copied in a similar, empty box immediately beneath the stimulus box. ’

Results

The dependent variables in this study are the relative frequencies of stroke directions and stroke sequences. Since we are interested especially in how the two parallel lines were drawn as a function of the stimulus variables, we concentrate on the order and direction of their execution in relation to the two other segments. However, for an impression of the effects of the three major stimulus variations, first consider the execution of the main axis I23 I of the pattern as a function of its orientation. Fig. 2 presents probability p(23), i.e., the relative frequency of drawing I23 1 as 23 (from (2) to (3)). It is seen that the large effects of Stimulus Orientation are different for the two Mirror Images. Thus, the performance direction of the stroke repre- senting segment 123 I is dependent not only on its own orientation but to a large extent also on that of the adjacent segments I12 I and I34 I.

Another analysis reveals that there is a high probability of threading, I1234 I being performed as three joined strokes, either as 1234 (41%)

or as 4321 (43%), together making up 84% of all performances. There is a strong global tendency here to perform these sequences left-right and top-down. Returning to fig. 2, we see that there are also differ- ences between the Parallel Forms. The probability of 23 is higher in

3 At the start of each trial, the subject’s arm was in an approximated standard position at 135

degrees to the table edge. The patterns to be copied were 25 cm from the bottom of the digitizer, which coincided with the table edge. Subjects held the pen above the centre of the next

response box and waited for a tone before starting to draw. Following this tone, subjects had 3 s to complete the copying task; this interval was marked by a second tone. There was a 2-s rest

before the next starting tone was presented.

A.J. W.M. Thomassen et al. / Graphic stroke sequences 75

(a) (b) Stimulus prototype Coding labels

A stroke sequence Coded sequence Parallel forms

Orientations

Positions Sizes

+e +>/Y>

J Fig. 1. (a) Prototype of the stimulus pattern, its coding labels, an arbitrary stroke sequence, and

the code for that sequence (This prototype has a value of 1 on each of the five variables). (b) The

variations applied to the prototype pattern along five dimensions, making up the set of

2 x 2~ 8 x 2 x 4 = 256 patterns. According to this factorial design, there were 128 patterns of

each Mirror Image, 128 of each Parallel Form, and 32 in each Stimulus Orientation. The

depicted variations have a value of 1 on each of the five variables, except for the illustrated variable if a different value is stated there.

Parallel Form 2 than in Parallel Form 1 (F(1,14) = 27.98; p < 0.01). This important finding will soon receive more attention.

Before turning to the execution of the parallel segments, we will also look briefly at the strategy of anchoring. Segment 156 I, which may or may not be anchored to I23 1, is an obvious candidate for such a strategy. As seen in fig. 3, 156 I is nearly always copied as the fourth and last stroke of the pattern, i.e., after 123 I has been completed. Predominant in all movement directions is 56, i.e., the anchoring mode of I56 I (t(14) = 3.20; p < 0.01; see fig. 4). Having observed this strong anchoring tendency, we are now prepared to consider the parallel performance of I56 I in immediate succession either with

76 A.J. WM. Thomassen et al. / Graphic stroke sequences

o- 1 I 1 I I I I 12 3 4 5 6 18

1 I I 100 -

s m

50 - c\i - n. 25-

o- I I , I I 1 I I 12 3 4 5 6 7 8

Stimulus Orientation

Fig. 2. Probability of the performance of segment 123 1 as 23, plotted as a function of Stimulus

Orientation and Parallel Form, separately for the two Mirror Images. Stroke 23 is more likely

under Parallel Form 2.

2400 ," 2 " 1600 rcI 0

4 800

kzz

0 12 21 23 32 34 43 56 65

Coding labels

Fig. 3. Number of cases in which each of the four segments is copied in each ordinal position

(digits above the tallest bars). 12 or 43 are mostly first, 23 or 32 second, 21 or 34 third; these data reflect the strong threading tendency, resulting in 1234 or 4321. The last stroke is nearly always

156 I, where 56 (anchoring mode) dominates over 65.

A.J. WM. Thomassen et al. / Graphic stroke sequences 71

-56 a------a 65 I I I 1 I I

:\J=:

‘, b____-o-____q-- .-’

1 I I I I 1 2 3 4 5 6 7 8

Movement Direction

Fig. 4. Probability of drawing parallel segment 156 1 as 56 and as 65, plotted for the two parallel

forms as a function of movement direction. A large proportion of the data is explained by

anchoring, which is prevalent in all directions, even in the non-preferred directions (3, 4, 5, 6), which are mostly avoided altogether in non-anchoring.

) 12 1 in Parallel Form 1, or with I34 ( in Parallel Form 2. From fig. 2 it appeared that I23 I is performed more frequently as 23 under Parallel Form 2 than under Parallel Form 1. The same difference holds for ( 12 1, where 12 is more frequent under Parallel Form 2 than under Parallel Form 1 (F(1,14) = 19.76; p < 0.01). The most likely reason, which is also suggested by fig. 3, is that when I12 ( is paralleled by I56 I, this tends to induce the copying of I12 1 immediately prior to 156 1, and in the same direction as that stroke in its anchored mode, i.e., as 21 preceding 56. Again, identical relationships hold with respect to 134 1, where 34 is more frequent under Parallel Form 2 (F(1,14) = 22.94; p < 0.01). Similarly, 21, 32, and 43 are more frequent under Parallel Form 1. In all these cases, the copying sequence tends to proceed towards the parallel pair, either to 21,56 or to 34,56. Of all parallel performances (N = 2165) a total of 1842, or 85% consisted of the latter two stroke sequences (see table 1).

The combination of threading (i.e., pen-down continuation of) the three-stroke sequence (1234 or 4321) ending in the first parallel (34 or 21, respectively) with the opportunity for subsequently anchoring the second parallel (56 I as 56 onto (23 1 provides a strongly facilitating condition for parallel performance. This strategy is significantly fa- vored both under Parallel Form 1 (&X1,14) = 15.15; p < 0.01) and under Parallel Form 2 (F(1,14) = 14.64; p < 0.01). Although this is not the only way to achieve parallel performance, anchored drawing following three-stroke threading may be regarded as the optimal

78 A.J. W.M. Thomassen et al. / Gruphic stroke sequences

*____* lstt2ndt3rd - 4th I I I I I I

I 1 I I J 1 2 3 4 5 6 7 8

Movement Direction

Fig. 5. Probability of drawing the terminal segment in a pattern as a function of movement

direction. The fourth stroke, contrasted here with the mean of the first three strokes, is more

frequent in preferred directions (1 , 2, 7, 8) and less frequent in non-preferred directions (3, 4, 5,

6).

condition, as is shown in table 1. From the table it also appears that non-anchored parallel performance increases sharply when threading entails two segments instead of three. A two-tailed sign test across subjects confirmed the significance of this effect (N = 15; x = 2; p < 0.01). This suggests that in a minority of the cases (549, or 14%) the pattern is parsed differently, not as three threaded strokes plus a separate one (3 + l), but as two threaded strokes plus two separate parallel strokes (2 + 2). Following such parsing, anchoring of (56 (

occurs only in about half the cases (266, or 48%), probably depending on the orientation of the stimulus pattern. The very strong (92%) tendency of parallel performance following the presumed 2 + 2 parsing apparently competes with the planning of anchoring, rather than being integrated into the planning of the sequence in which anchoring

Table 1

Incidence of anchoring and parallel performance as a function of threading.

Anchoring

+

+

- _

Total

Parallel performance

+

_

+ _

Number of strokes threaded

3 2 1

157.5 237 30

540 29 1

7 267 49 1088 16 1

3210 549 81

Total

1842

570

323 1105

3840


is also incorporated. To the finding that a total of 1088, or 34% of the three-stroke continuations precede a non-anchored, non-parallel fourth stroke we will return below. Here it suffices to note that a large proportion of the stroke sequences reflect the anticipation of parallel performance of the two parallel segments as the two final strokes. The appropriate conditions to achieve this following parsing of the pattern are created earlier in the sequence by threading and anchoring.

Let us now consider the movement directions followed in the course of the copying sequence. On the basis of the literature and of our own earlier findings (see references above) we distinguish between preferred and non-preferred movement directions in righthanders, as follows. Preferred are the straight downward and all rightward directions (i.e., 270 and 315, 0, 45 degrees, corresponding to directions 7 and 8, 1, 2, respectively). Non-preferred are the straight upward and all leftward directions (i.e., 90 and 135, 180, 225 degrees, corresponding to directions 3 and 4, 5, 6, respectively). In fig. 5 we see that the general tendency is, of course, to choose. the preferred directions 1, 2, 7, 8. Now, looking at the first, second, third and fourth stroke across all patterns, it appears that the fourth stroke has the highest frequency in preferred and the lowest in non-preferred directions. Two- tailed sign tests comparing the fourth stroke with the first, second and third stroke across subjects showed that this difference was significant in each case (N = 15, x: = 3, p < 0.05; N = 15, x = 2, p < 0.01; N = 15, x = 3, p < 0.05, respectively). This finding supports the notion of a tendency to terminate a movement sequence in a relaxed mode. The above-mentioned proportion of 34% non-anchored, non-parallel performances of 156 1 following three-stroke threading (table 1) can for a large part be explained by this tendency competing with that of anchoring and parallel performance. This interpretation finds support in fig. 4, where non-anchoring performance 65 of (terminal) segment 156 1 appears almost exclusively in preferred movement directions.

Discussion and conclusion

We have observed largely varying stroke sequences as a function of pattern orientation and stimulus structure. A major determinant of stroke direction and stroke order appeared to be the mapping of the orientation of the pattern onto that of the biomechanical system with


its preferred (down, rightward) movement directions. More interest- ingly, systematic effects were observed as modulations of the general preferred-direction tendency. The economic advantage of using the same motor program twice (with only a minor translation) appears to be exploited in a large proportion of the sequence organizations. The dominant tendency is drawing a threaded three-stroke sequence first, followed by the fourth stroke, preferably anchored to the second. The prevailing strategy here is to start the three-stroke sequence at the extreme which is furthest removed from the fourth segment, so that the third stroke immediately precedes the final one, for which the same motor specification is then used once again. The first chunk may also comprise two strokes. In all cases, such planning may be seen as a hierarchical process in which the starting point of the first chunk is influenced by the location of the last, and in which the movement direction of the final stroke is largely determined by that of the penultimate one. Especially with respect to this final stroke, there is also a considerable bias to follow a preferred movement direction.

We may conclude that the structural features of a geometrical pattern (e.g., the presence of parallel segments) and the orientation of the pattern in relation to that of the effector system exert a combined, permeating influence on the organization of the entire movement sequence. In general, subjects anticipate the repeated use of a motor program by appropriate parsing and by adopting a stroke sequence which follows the rules of threading and anchoring and allows the implementation of this repetition economy. In a minority of the cases, one economic strategy (threading, anchoring) is traded off against another (parallel performance, preferred directions). Furthermore, subjects tend to terminate stroke sequences by a movement in a preferred direction, which seems to reflect an increased sensitivity of the final segment to biomechanical constraints. Although a full account of all the findings of the experiment requires more space than is available in the present paper, we conclude that the above results constitute strong evidence for the effective anticipation of economy in graphic behaviour. The (higher-order) advantage of repeated use of the same motor program is generally foreseen and taken into account in the selection of a stroke sequence. This, however, is also subject to the (lower-order and strategic) constraints implied in anchoring and threading and, most severely, to the (lowest-order) biomechanical constraints reflected by direction preference.


Above, we noted that studies on the selection of successive segments in complex movement sequences are few and far between in the research literature. Some most intriguing papers studying the constraints on the selection of hand grip have, however, recently appeared from Rosenbaum’s laboratory (Rosenbaum et al. 1990; Rosen- baum and Jorgensen 1992). The data from these experiments are fully consistent with the present results. They too show that anticipation of the terminal state of a complex action determines the specification of the initial movement segment, and that there is a tendency for a previous motor specification to persist in the subsequent action. These features of complex action presumably reflect a principle which mini- mizes the cost of preparing and executing complex movements.

It may be hypothesized that economy plays a key role in all forms of behaviour. Spending the least amount of effort in the attainment of a satisfactory goal is probably also a principle of graphic behaviour. In the present experiment we have seen examples of different types of economy: drawing under optimal control-by following preferred movement directions, omitting pen lifts by threading, minimizing spatial uncertainty by anchoring, repeating the same movement specification by parallel performance, and terminating the action in a relaxed mode by drawing particularly the final segment in a preferred direction. The efficient planning and execution of a movement sequence, whether it is a sequence involving 2-D graphic action or action in 3-D space, necessarily implies the anticipation of such economy and the creation of suitable conditions where needed and possible. The present paper illuminated this for the domain of graphic performance.

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Documents

Economy and anticipation in graphic stroke sequences *