In her estimation, this has been a bumper season for crop formations. It started late, because the crops themselves were late after the cold spring; but it flowered into a splendid harvest as amazing shapes appeared in wheat and barley across the chalk downlands of Wiltshire, Hampshire and Berkshire, with outliers as far afield as Somerset and Nottingham.
Some of them, certainly, were man-made. There was no secret, for instance, about the twin circles joined by a bar - a kind of dumb-bell - which manifested themselves on the farm belonging to Tim and Polly Carson near Alton Barnes. These were laid out one night by two young Germans, whose addiction to the creation of formations is such that, with the agreement of the farmers, they come over every summer to try some new design.
Yet in Lucy's view many formations derive from natural causes. One of this year's most remarkable was the huge pattern close to Stonehenge which appeared early in the evening of 7 July. The pilot of a light aircraft coming up from Exeter flew over the field as he was starting his descent into Thruxton, some five minutes away. At that moment the wheat was unblemished. When he returned within half an hour, the corn below him was imprinted with an astonishing array.
Experts described the formation as a Julia set, or fractal image (one which can be divided ad infinitum): several dozen circles of swept-down corn had appeared in a lazy curve reminiscent of a lizard seen from above. The circles graduated in diameter from a couple of feet at the tail to 15 yards at the head, and the whole layout was 900 feet long by 500 wide. As Lucy remarked, it was inconceivable that humans could have made it unobserved, and in fewer than 30 minutes .
The same applied still more emphatically to an even bigger formation which appeared at the foot of Windmill Hill, near the village of Yatesbury, on the night of 1 August. This was another fractal image, but a triple one, with three lizard-like curves of circles swinging into a single head, the whole more than 1,000 feet across.
When Lucy first visited this site, two days later, the swept-down corn had "a marvellous bounce to it" - the sure sign (in her view) of a formation made by natural forces. In man-made circles the crop is crushed and flattened, but in others it is left fluffed up in an even blanket six or eight inches off the earth. The destructive agent appears to be a sudden burst of energy which softens the stalks of the corn just above the soil.
When I visited the site, I was immediately struck by the fact that from ground level, in a field set on only the gentlest slope, it was impossible to see the whole formation at once, or to get any idea of its shape. Only when we flew over could I appreciate that the whole was laid out with astonishing elegance and precision.
A veteran of many summers' research, Lucy is cautious with explanations. "Everyone thinks up the wildest ideas," she says. "For example that the triple Julia was somehow created by a Ministry of Defence satellite operating bomb-disposal equipment." She mentions ley lines, and believes that Windmill Hill, Silbury Hill and the like are "power-packed places".
She herself believes that natural formations are caused by abrupt discharges of energy, and she can report many curious happenings. Last year, when two labradors entered a circle, they ran amok and attacked the nearest human; outside the formation again, they reverted to their normal sloppy selves. This time, several people who went into the Stonehenge formation felt extremely ill, and one man - a molecular biologist, used to working with radiation - staggered out claiming that he had been irradiated. Over the next few days the bodies of visitors passing through seemed to drain off the energy, but grains of wheat still carried a high charge.
Flying low along the line of the Ridgeway - the ancient track that follows the top of the Downs - we came eyeball-to-eyeball with the Uffington White Horse, with Iron Age hill forts, with prehistoric burial mounds. Out in the plain to the south the megaliths of Avebury and Stonehenge sentinel. Could it be that the forces which shape crop formations today are the same as those which made primitive people raise their monuments in this wide-open landscape?