Report on Pulvinus Length Measurements

Objective

‘Pulvinus length increase’ in crop circle formations has been reported many times by other researchers, in particular by the BLT team (Burke, Talbott and Levengood). Due to the amount of field work involved, the number of samples taken is usually limited. The two circles under discussion in this report were both sampled in 27 positions, all circularly symmetric, while ±20 stems were taken per sampling point. Objective was to investigate the average pulvinus length per sample as compared with controls taken in the upright crop, and in particular the variation of the average pulvinus length over the physical imprint of the two formations, so as to reveal any clues related to the symmetry of the energies involved in crop circle formation.

Background

On Monday June 7, around 1:30 AM, an eyewitness (known to the author) saw a small light in the sky, which looked like a bright star. He was standing in his bedroom, looking out over the field behind his house. Then he noticed, however, that the light was moving, and actually seemed to be quite close. The colour of the light was a very faint pink (almost white). Suddenly, in just a few seconds, the light transformed into an elliptic shape. The eyewitness noted how the air around it seemed to tremble, as if it were hot. Then the light slowly fainted and disappeared. The eyewitness ran into the field, where he discovered a circle of flattened crop. The crop, the soil and the air felt physically warm. Next morning, he noted that a small (two feet diameter) circle of flattened crop had appeared, adjacent to the larger one.

On Saturday June 12, 1999, a second formation appeared at a stone’s throw from the first one. Around 1:00 AM, the same eyewitness noted a short light flash above the field, "as if a photograph were taken". The light seemed to emerge from a single point, flashing down on the field, and was of a very faint bluish colour. Upon inspection, the second circle was found, which also felt physically warm.

Methods

Sampling

On Sunday June 13, stems from the three formations were cut close to the ground, wrapped together with adhesive tape, and labelled. The sampling diagram is sketched in Fig. 1. Three sample ‘lines’ of nine sample ‘points’ were taken per circle. In each circle, one sample line was aligned North-South, the other two were taken at plus and minus 60 degrees angulation with respect to the North-South line. Diameters of the circles varied between 860 and 900 cm. Samples were taken at equidistant intervals of 150 cm, starting at one edge, with the last samples at the opposite edge. (Consequently, the distance between the last samples was sometimes slightly less than 150 cm.) However, the first two and last two samples in a line were taken as close to one another as possible, in such a way that one of them was taken in standing crop, just outside the physical imprint, and the other in flattened crop, just inside the physical imprint (see Fig. 1).

Two samples were taken from the small adjacent circle (a few feet west from the June 6 circle, not indicated in Fig. 1), one at the edge, and one in the centre.

A total of 9 control samples (with ± 20 stems per sample) were taken in the standing crop. CO1 was taken at 3 meters south from the southern edge of the southern circle (left circle on the diagram). CO2 at 10 m south of same reference, CO3: 20 m, CO4 30 m. CO5 was taken exactly in between the two circles. CO6 was taken at 3 meters north from the northern edge of the northern circle (right hand circle on diagram). CO7: 10 m, CO8: 20 m, CO9: 40 m (not thirty!).

All controls were taken about six feet west from the tramline, i.e. not through the circles’ centers.

FIGURE 1 - Sampling Diagram

Measurements

All samples were dried for several months, before pulvinus length measurements were performed. All stems of each sample were clamped between iron pins for alignment, and photographed with a Sony DSC-F55E digital camera. With 1600x1200 pixels, the effective resolution of the photographs was better than 0.1 mm per pixel for all acquisitions. A 2.0 cm vertical strip was glued on the clamping block, and used for calibration purposes.

A computer program was written (see Fig. 2), which assisted in the measurement of pulvinus length. First, all photographs were reduced to 256 shades-of-grey, after which all pixels p_x,y (ranging from 0 to 255) were transformed according to

p’_x,y = | p_x,y+n – p_x,y-n| [1]

where n was adjustable (n=2 was used during the entire analysis). Next, the computer algorithm would find one positive number L₁ and one negative number L₂, defining two line elements with adjustable length of 2m straight above and below any indicated point (x,y) of interest (being the centre of the pulvinus) for which the contrast values

[2]

were maximised. The values of m were adjusted so as to match the width of the pulvini. Pulvinus length was taken as the absolute value of L₁-L₂. In case of poor contrast, or severely bent pulvini, the program allowed for manual correction by indication of two points, the distance between which was recorded. It must be noted that both in the case of computer assisted and manual measurements, the measurement accuracy depends solely on the visual judgement of the user. By measuring the same sample set several times, an indication of the accuracy for average pulvinus length values was found to be 0.05 mm.

FIGURE 2 – Screen Layout of the software package during use

Analysis

Graph 1 shows the determined average pulvinus length values of the nine control samples. Graphs 2a-c show the average pulvinus length across three cross-sectional lines in the large June 9 circle. Graphs 3a-c show the average pulvinus length across three cross-sectional lines in the June 12 circle. Graph 4 shows the average pulvinus length just inside the edge (g1) and in the centre (g4) of the small June 12 circle, which was found adjacent to the large one. Green and yellow bars indicate average pulvinus length, red bars indicate standard deviation for each sample.

GRAPH 1 GRAPH 2A

GRAPH 2B GRAPH 2C

GRAPH 3A GRAPH 3B

GRAPH 3C GRAPH 4

Earlier it was suggested by the author, that pulvinus length increase might be a thermo-mechanic effect induced by an electromagnetic point source located at finite distance above the field. Assuming that the pulvinus length expansion is proportional to the electromagnetic radiation intensity on ground level, this hypothesis can be verified from the data by matching the pulvinus length increase (formation length minus control length) to 1/r², where r² = h² + d², with h the (assumed) height of the point source above the circle imprint and d the distance of the sample point from the circle’s centre.

Obvious candidate for a ‘BOL analysis’, from the shape of the pulvinus length curves, is the June 6 circle (Graphs 2a-c). Because of the two local minima in Graph 2a, one does not expect a good fit for the corresponding data set (A). This was in fact confirmed, a maximum Pearson coefficient of R² = 0.55 was obtained for h = 3.1 m. Graph 5 shows the results for Graph 2b (data set B). Setting the parameter h to a value of 4.1 meters, a very good correlation with a Pearson coefficient of R² = 0.99 was obtained. For Graph 2C (data set C), a maximum Pearson coefficient of R² = 0.85 was obtained for h = 6.6 m.

GRAPH 5

Discussion

Graph 1 shows that the average pulvinus length of the controls was in the order of 2 mm (exact value: 2.01 mm).

The June 12 circle (Graphs 3a-c) revealed a higher average pulvinus length value (2.24 mm), i.e., an increase of 11% compared with the controls. Taking into account the brief period between the formation of this crop circle and the sampling (one day), the pulvinus length increase is higher compared with earlier reports of gravitropism related effects in hand made formations (BLT reports 27 and 86).

More interesting are the results shown in Graphs 2a-c. Two remarkable facts are revealed:

1. An average pulvinus length of 4.32 (standard deviation 0.37) mm in the centre of the circle, i.e., an increase of 114% compared with the controls. (Graph 4 even shows an average pulvinus length of 4.38 mm in the centre of the small adjacent circle, i.e. an increase of 118% compared with the controls.)
2. A perfect, twofold, highly detailed symmetry with respect to the centre, in each of the three sample lines.

Even more remarkable is the fact that the actual shapes of the Graphs 2a-c, despite their identical symmetry, are all different. This means that there is only in some approximation a circular symmetry in the pulvinus length distribution, which is better expressed as a multifold twodimensional symmetry. This fact might indicate, although somewhat speculatively, that the energy responsible for pulvinus length increasing had symmetry properties similar to a rotating twodimensional beam with twofold symmetric, time dependent intensity distribution.

At the same time, the results shown in Graph 5 indicate that the pulvinus length increase corresponds perfectly to the radiation intensity on the ground resulting from an electromagnetic point (or spherically shaped) radiation source at a height of 4.1 meters above the ground. This fact is interesting because of the eye witness’ statements, explicitly mentioning the involvement of ‘a small light’, and ‘trembling air as if it were very hot’. The fact that this small light transformed into the "elliptic shape" could explain why the match is not perfect in all cases. In fact, from these sort of experiments with many unknown environmental boundary conditions, one would not easily expect a perfect match of experimental data with (simple) theory.

Conclusions

The symmetry found for pulvinus length increase in an extensive amount of sampling data from one of the investigated crop circles is remarkable, and seems to lack trivial explanations. Moreover, the pulvinus length increase of 118% is an order of magnitude more compared with results from control studies performed earlier by the BLT team.

The results shown in Graph 5 indicate that the pulvinus length increase in one of the circles corresponds perfectly to the radiation intensity on the ground resulting from an electromagnetic point (or spherically shaped) radiation source at a height of 4.1 meters above the ground. The high correlation coefficients seem to provide physical evidence of the statements made by the eye witness, mentioning the involvement of ‘balls of light’ and ‘heat’ .

Consequently, the observations described in this report are in agreement with the hypothesis that pulvinus lengthening in crop circles is a thermo-mechanic effect, induced by heat from a point source with (at least some) electromagnetic properties.

Eltjo H. Haselhoff
Dutch CCCS.