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Aug 30, 2011 8:37 PM CST
|These people laid out a garden to look like the arms of our Milky Way spiral galaxy:
(You may have to wait a while for the first picture to download, the one labeled:
"A view from above of the entire Milky Way Galaxy, looking west. "
Theirs is more graceful, but here's a trick for laying out a perfectly regular spiral with constant-width arms, in case you want constant-width beds and constant-width walkways:
1. put something big and round in the center, like a barrel or 10-15 stakes in a circle
2. the circumference of this central circle is the distance between successive turnings, call it the spacing of the arms.
3. Now wind a long string or rope around the center. Go around as many times as the number of turnings you want the final garden spiral to have. Three turnings with 3 foot spacing will be 12 feet across, plus perhaps a central circle.
4. Now gradually unwind the string from the central circle, holding it taut from the center to where you're holding the free end.
(It will unwind tangent to the central circle, not straight out - that's OK.)
5. Push in markers, sprinkle lime or drop pebbles where the end of the rope is, every few steps. Then dig the bed in a smooth curve following the markers.
6. (Maybe mark the curve roughly, and do the digging and amending roughly at first, but later repeat the unwinding process with two spots marked on the rope, to set the walls into precise, smooth curves. But then you'll have to get the central circle in the exact same size and in the exact same spot when you re-survey it!)
Here are some possible sizes:
- a 10 inch diameter inner circle would give 32" spacing:
. . . . . . . . . .18" wide beds, 12" walkways and 1" walls
- a 12 inch inner circle would give 3.14 feet spacing:
. . . . . . . . . . 24" wide beds, 12" walkways, and 3 / 4" walls.
- an 18" diameter circle would give you 56" spacing:
. . . . . . . . . . 36" beds, 18" walkways and 1" walls.
( Diameter of inner circle = spacing of the arms in inches divided by 3.14.)
You might not want the spiral beds to wind all the way into the center: the innermost turning looks cramped. Maybe plan a central open circle for chairs, or a circular central bed with a walkway most of the way around it, that the spiral bed emerges from. Or run a much narower walkway or stepping stones into the central circle, to continue the pattern without crowding. Or plant something tall and narrow in a spiral in the central circle.
The above is just an Archimedean spiral, with constant-width beds and constant-width walkways.
It isn't as graceful as the beautiful constant-angle "logarithmic spiral" seen in the nautilus shell, hurricanes and some plants. Other names for the pretty one are "equiangular spiral", "growth spiral" or Bernoulli's name for them: "Spira mirabilis", "the marvelous spiral". He wanted one on his tombstone, but someone goofed and gave him the easy-to-draw one instead!
I don't know any trick for drawing a clean, big logarithmic spiral. Maybe if you left 10-20 feet of extra string beyond the point where you started planting markers, and let a constantly-increasing amount of string slip through your fingers with each step. I don’t have enough math to figure that out!
Or you could hint at the more graceful form by making just the last turning "open out" some. Perhaps leave the walkway 12" wide, but give it two widening borders of white pebbles.
I think spiral galaxies can look either way, or be constant-width near the center, and more logarithmic on the periphery, especially when unraveling due to other galaxies passing too closely. When that happens, they reach out towards each other, or even unravel, as if reluctant to let go of their neighbor.
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