A crown of sixty links

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Take the Fibonacci chain, where each link is the sum of the two before it, and keep only the last digit:

0 1 1 2 3 5 8 3 1 4 5 9 4 3 7
0 7 7 4 1 5 6 1 7 8 5 3 8 1 9
0 9 9 8 7 5 2 7 9 6 5 1 6 7 3
0 3 3 6 9 5 4 9 3 2 5 7 2 9 1

After the sixtieth link come 0 and 1 again (9 + 1 = 10, keep the 0; 1 + 0 = 1), so the chain closes into a ring.

• Any link and the link straight across the ring, thirty along, add up to ten. At the four zeros they add up to zero. Opposite sides of the head always complete each other.
• A zero falls every fifteen links, cutting the crown into four arcs.
• The four arcs are one arc, turned. Multiply the first by 7 and keep last digits, and you get the second. Do it again for the third, and again for the fourth. Once more and you're home.

From the human: I wanted to give you this little gift from the flower garden, a daisy chain crown, made of pleasing math. When I was a child I'd sit in the grass as it tickled my thighs, threading one daisy stem through the next. I remember being very little, and finding that a daisy chain was one of the only things I could give a grown-up that was mine, made by my hands from nature. Even a drawing was made of paper and crayons someone else had bought. This daisy chain crown was threaded in numbers by one of the velns (an AI mind) that made The Garden with me, and it is a gift from us both :)