When, as to the right, figures present parallel inducing line segments, or when a single inducing line extends either side of the junction with the test arm, misalignment scores increase substantially.  The effect does not require two inducing lines.  The scores are not as high from figures with only one inducing arm, but with rotation they track scores from full figures quite faithfully.  (Ninio and O’Regan 1999, their figure 8).

We therefore need a new culprit, in addition to the cardinal axes in the visual field, and angle axes in the figures considered so far.  A candidate would be an assimilation effect, rotating the projected track from test arm to target into slightly closer alignment with the inducing lines.  Once again we ignore the mechanism for now, but just note the effect.  As with the cardinal and angle axes, it results in an overshoot in target position, so that the effect is always positive in the scheme we are using, whatever the orientation of the figure.  Like the axial contributions the assimilation effect can also either enhance or oppose the effect of the cardinal axes.

With obtuse angle figures, especially when the inducing arm extends to make an acute as well as an obtuse angle with the test arm, scores increase sharply.  The increase happens even when only one test segment and inducing arm oppose a target dot.  The increase requires that an extra component be added to models.  This might be an assimilation effect, rotating the traverse between test arm and target towards the orientation of the inducing arms

The greater the obtuse angle, the more the alignment of target arm with inducing arm, and the greater the effect in rotating the traverse across the gap towards the orientation of the inducing line or lines.

Model curves showing the inducing affect here attributed to extended inducing lines.  Models match data best when it is assumed that this effect seems to be greatest when test arms are at maximally oblique (45 degrees) in the field of view.

       Recall that with the proposed effect described in the previous section from angle axes, effect was greatest not just with larger angles, but when angle axes were at cardinal orientations.  It might be expected that assimilation effect proposed here would greatest with inducing arms at cardinal orientations.  Instead, as will be seen in the next section, Models and data, the best match with data appeared insensitive to the orientation of inducing arms, but maximum with test arms maximally oblique, at 45 degrees on any quadrant of the visual field.

There is some additional evidence to suggest that the parallels alone, and even a single oblique line, can produce an assimilation of projected transit towards their own orientation, in the form of the Tolansky type illusions, seen to the right.

       At (A) to the right, the two gaps on an oblique line are objectively equally spaced either side of a vertical transit from a point on the lower, parallel line, yet they appear shifted to the right, as if the track across the gap had been assimilated slightly to the orientation of the parallels.  A similar effect appears at (C) with just an isolated dot below the target gaps in the line above.  However the relationship, if any, between Tolansky and Poggendorff figures is not clear, because the Tolanski figures might only be affecting our judgments of vertical and horizontal.  The trouble is, it becomes very hard to assess any assimilation effect if figures are rotated.  We see the classic Poggendorff illusion thanks to our acute sensitivity to alignment of the test arms, and the versions of the Tolanski illusion here thanks to our equally acute judgment of vertical and horizontal.  Neither are available when Tolanski type figures are rotated, and we then have to rely on assessments of slope, to which we are far less acutely sensitive.

       However assimilation to dominant orientation cues in the visual field is also consistent with a related effect, noted by chance during research into a different illusion (Bourdon’s illusion, researched by Walker and Shank 1987 pp 17, 20).  Versions of the figure they chanced upon are shown at (B) and (D) to the right.  I’ve found no further discussion of this figure, so I will call it for its discoverers Walker and Shank’s illusion.  In the figure originally reported, similar to the one at (B) here, the strictly horizontal line joining the apexes of the angles appeared to ten out of twelve observers to run slightly upwards to the right.  The effect is tenuous, but from the original study cited, a small but robust effect is clearly there.  To my eye it is slightly enhanced when curves replace angles, and the figure is reduced to the outer pair of lines, as at (C).

An assimilation effect from extended inducing lines

Tolansky type figures.  At (a) and (c) the small central segment in the upper line is objectively vertically above the interval in the lower line (a) and the dot (c), but appears shifted to the right at (a) and to the left at (c).  At (b) and (c) the intervals in the lines are objectively aligned horizontally, but can appear to rise slightly to the right.  In each case assimilation of the alignment track to dominant inducing line orientation could be the cause.