Monday, June 4, 2018

Figuring out the Maths of an Operculum

Following on from the previous video of Russian lady crocheting a spiral in tunisian stitch.  insert---



I am thinking about how to crochet this operculum (diagram of real thing.) 
 It was maybe found on the beach at Little  Bay, Sydney, 2015.
See early post, of Dec 28, 2014, for story of my visit to Little Bay Beach.
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Actual size is 36mm long and 30mm wide.  
It must have come from quite a big Turban-type shell, maybe 10 cm or 4 inch long?


I have made a tentative model for the seashell in a recent framed display posted previously, (please scroll down.)
Shell model was 15cm (6inches) x 10cm across;
operculum made was 60mm long and 45mm wide.

 Must give an instruction Pattern for how to make them, asap.
 Am busy and slowing down-  age 72.  Still alive and well.

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More.  31/8/2018.
Finally I have printer/scanner working,  and hope to make more posts.




Please click on image, to see it larger.  Right click for options to copy on to Word, or save on to downloads, etc then print.
A left handed person would crochet the spiral in the correct orientation face side up.
A right handed person would have to use the other side up as orientation.
 It looks like one has to work twice in each loop and a few times three times in the same loop (ones marked blue), to achieve numbers.  I need to redo this design, for often the operculum is longer than this.  But it is  a start because one begins by wild guessing, then one fine tunes the work.
Outer can be 72 (which is half of 144)  the next spiral in is 34, then 21, 13, 8  or so.  Theoretically.  One can guess the maths might be eg another  one- ....8, 13, 21, 44.......  the outer being half of 89 in this one.  fibonacci helps us guess.

 A simplified way is to Begin with 8, then twice in each to get 16, then twice in each to get 32,  then twice in each to get 64 plus a few three times to get say, 72.
Use a different coloured thread to mark the end of each spiral row.
The stitch is the Tunisian spiral, as shown in previous video made by Russian lady.
You can lengthen the piece by making the widest, 11 loops into say 13 or 14 or more loops.  graduated.  Experiment.
 I have two pieces which I made for a start but they only had about 55 in outer ring.   A thicker yarn (crochet cotton 3 ply) made a larger model than the finer mercerised crochet cotton they used to make doilies once upon a time.



However.  It is one thing to make something linearly.  It is another matter to do it swirlwise, as we see the actual operculum has such a structure.



As for Sunflowers.  They grow swirlwise.  I wrote posts, December 2012, on theoretical sunflower designs.  Here is a computerised pattern I found on google images, but I coloured them in as if each row came out from the centre,  only the seeds are flat and fit themselves in tight at an angle.  Another version shows 34 in subsequent rounds.


 I have found  good maths fibonacci especially on Sunflowers. YouTube videos by Mathologer.
 He introduces the Tribonacci Series.! amongst many other original ideas.
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