Hackpen Hill

NOTES FROM THE SPOT I didn't go inside this formation, though I saw it from the road. I'm inclined to say this is my favorite of the '99 season, at least when it comes to estethical values. In addition to the sheer beauty of the geometry, the "craftsmanship" is extremely high quality! GEOMETRY The impression you get first is of a twisted doughnut with three crescent blades growing out of it. Or you could just see it as a spiraling vortex form. To me the shape suggest clear clockwise motion, though I completely understand if somebody prefers to see it anti-clockwise. It's funny how the "blades" turn from sharp and solid into soft and loose when you change the rotation direction, try it! Despite the first impression, the formation actually consists of a central circle with three simple spirals, each made of four semicircles (which means they are not actually spirals at all). In addition there is a very thin ring, which at first glimpse would seem to be a large circle enclosing the whole shape. But it is in fact made of three parts, each a portion of a circle defining the inner arc of the "blade". Let's take a look at the circular structure... Follow the logic with the help of the following diagram:

Place the mouse pointer on the diagram or click it in order to see the circles more clearly!

1. Make circle A. 2. Make a circle with a double radius, centered on the edge of A -> B. 3. Make again a circle with a double radius, C. 4. Place a new circle on the edge of A (1) in 30 degrees so that it meets the edge of circle C (2) ->D. 5. Place another circle again 30 degrees from A (5), so that it meets both D (3) and the diameter defined by C (4). 6. Lay down the central circle. 7. Continue laying down the outer edge of the spiral, following circles B and C (green), from 'a', through 'b' to 'c'. 8. Lay down the inner edge, following D and E (orange), from 'd', through 'e', all the way to 'f' (this completes the part drawn in black in the first diagram). 9. Repeat steps 2 to 8 (apart from step 6) three times, revolving 120 degrees for each go.

Circle A is one fifth in diameter of the overall diameter of the formation. B is double this, C is quadruple. These are exact ratios based on the unfolded geometry. Furthermore D is exactly 9/8 of B. If you were able to follow this procedure, you noticed that at no stage was there any element added not related to the previous elements. Number of circles used in the formation is 13 or 14 (depending whether you count the large perimeter circle or not, after all it is not included in the final form). Number of "strokes" (for the plasma balls "painting" the crop) needed according to the previous procedure would be just 6 (though the width of the stroke should be then changed for the thin arcs between the blades - alternatively you need 9 strokes). Based on the videos shot from the light balls (Oliver's Castle, '96 and Barbury Castle '99), they seem to be able to split and then come together again. Hence one could also imagine the laying down happens in the following way: 1. Send the plasma ball in the middle of circle A and set it in a spiral motion, expanding towards the perimeter. Fill the space defined by the rounded triangle defined by the B circles. 2. Create two new plasma balls at the starting point of each spiral extension (like 'a'). 3. Let the first ball follow the circles B and C (green line), the second circles D and E (orange line). At point 'c' release the first ball. Let the second run all the way to 'f'. The same for each of the spiral arms. Can you Imagine all the six balls creating the formations simultaneously? (Hopefully I'll make an animation of this later) - Martin Keitel, 2000