This is what it looks like:-
This is how to make it:-
Supporting data:-
Please click on images to enlarge them.
We have here the Fibonacci Series plus the Half Fibonacci Series as landmarks along the torus surface, The algorithm is crochet once in 3 loops then twice in 4th loop. Plus minor adjustments at the end to effect the Fibonacci Series numbers most exactly. Sometimes I may be out by 1 or 2 or 3 stitches but I don't worry. Mutations. Lost concentration etc. I have given alternatives in Pattern. The actual model follows the beginning from 21 to 72 ok but I wondered what it would look like if I did 8 rows of 89, leaving out the in between 81........ = a different kind of "round".
Another thing to watch out for. The first chain row is often very tight compared with the body of work; so I used size 3.5 hook for the first chain row of 21. Then I changed to a size 2.5 hook for the rest of the work.
See the spirals........ begun at stage 21 row; a colour between every 4 loops and then the black right at the end (after 5 loops) . Funny how they diverge differently......
So a new try, to do the end of row differently.
Instead of smoothly working crochet from last loop to first on row loop, this way:-
crochet into last loop.
slip stitch into first of next row. AND work one crochet into the same stitch,
then proceed as usual till the end
where you MISS the last slip stitch and slip into the nest stitch, then crochet one into the same stitch. Keeping the black yarn at the end of each row between the loops, the line continues straight UP and not in a spiral!
Here I began with 13 chains then 2 chains, then single crochet into the 13 loops.
successive rows a previously described show the vertical line.
So next I increased in every 4th stitch/loop.
( sometimes I missed, and was a few stitches less....but no matter...)
Now I can see that it is the nature of the crochet stitch which gives the spiral.
Just out of curiosity I figured out how the numbers would increase if I did pure algorith 4 to 5:-
How
beautiful the numbers are!
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Please look at Facebook for Hyperbolic Crochet Reef. A new BOOK will soon be out; describing the Beautiful Mathematics involved. Also www.ted.npr.com The TED Radio Talks -- Margaret Wertheim has given a talk on the subject. I shall have to check it out correctly myself asap.
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Another website to look for is www.toroidalsnark.net.......(I think).....
Sarah Belcastro has crocheted a torus, and it has Spiral Pattern on it. I do have a picture of it somewhere.
Meanwhile, until next time, here are pictures of my land. Very busy time of year. Apple blossoms. I am very grateful.
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