Theoretical Fibonacci Ripples IAW the Protocols.

Insert 22/12 2016  here is the 377 model!



















Here is 2015 post....
The completed model has just been made, to 233.
The crochet rows segue perfectly with the recently published Eternal Protocols, all along the Fibonacci Series.  I have calculated up to 610 and it seems that the method continues further.  It would take too many hours of sitting crocheting to do more than the 233.
Work here is done with 3 ply baby wool and number 2 crochet hook.

More:-
27/12/2015
Please click on images to see more clearly.  You can scroll along images one after the other.
 Right click to save or print.
The numbers segue along beautifully.  That is how I made the model of the "ripples".
It is a bit tricky at the end of each row.  I do mark the spot with a different colour yarn.

Calculations for Concentric Circles (Ripples)

Iaw the Fibonacci Series.  Circumf = 2 x Pi x  r = 6.283 x r
Fn                    radius              r1 – r2             rows              
10946              1742.2 =r1       665.5               666                  
6765                1076.7=r2        411.3               411                  
4181                665.4               254.2               254                  
2584                411.3               157.1               157                  
1597                254.2               97.1                 97                    
987                  157.1               60                    60                    
610                  97.1                 37.1                 37                    
377                  60                    22.9                 23                    
233                  37.1                 14.2                 14                    
144                  22.9                 8.7                   9                      
5 5                    8.8                   3.4                   3                      
34                    5.4                   2.1                   2                     
21                    3.3                   1.2                   1                     
13                    2.1                   0.8                   1                      
8                      1.3                   0.5                                          
5                      0.8                                                                                                                                                                  

                                                                                        

Yellow marks the end of the row.  Note the first loop of next row is white, due to the nature of crochet the loop carries over to the next stitch.  One needs to be assiduous in counting.  Even a mistake of one stitch can put the work out.  It is gratifying when one comes to the end of each row with the correct number of stitches!

Here is diagram with each of the 6 segments being about 50 degrees from centre.  The half (7th) segment varies and seems to form a curve.  Does this have the effect of pulling the rest of the circumference into a spiral direction?  I wonder about the dynamics of real ripples and vortexes.

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 ok     - more work for anyone inclined to be interested......
I am keeping the images on this page small because you really do have to click on them to enlarge them and so see better.

Calculations for Concentric Circles (Ripples)

Iaw the Fibonacci Series.  Circumf = 2 x Pi x  r = 6.283 x r

Fn                    radius              r1– r2              rows             

10946              1742.2 =r1       665.5               666                 

6765                1076.7=r2        411.3               411                  

4181                665.4               254.2               254                  

2584                411.3               157.1               157                  

1597                254.2               97.1                 97                    

987                  157.1               60                    60                   

610                  97.1                 37.1                 37                    

377                  60                    22.9                 23                    

233                  37.1                 14.2                 14                    

144                  22.9                 8.7                   9                      

89                    14.2                 5.4                   5                      

55                    8.8                   3.4                   3                      

34                    5.4                   2.1                   2                      

21                    3.3                   1.2                   1                      

13                    2.1                   0.8                   1                      

8                      1.3                   0.5                                          

                                                                                                                                                                                       

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