Saturday, September 13, 2014

Combining the Fibonacci Series and the Half Fibonacci Series **





So we might have a new Series:-

0,  1,  1,  2,  3,  4,  5,  6,  8,  10,  13,  17,  21,  28,  34,  44,  55,  72,  89,  117,  144,  188,  233,  305,  377,  493,  610,  ...............

What does it mean?
We can make a Fibonacci Hyperbolic Fan Shape,  using gradual  increases,  as follows:-





Please click on images to enlarge them.

I've included the higher Fibonacci numbers,  just as an academic exercise.


The most exciting aspect of this development is that it is the Algorithm  4 to 5,
 ie  crochet 3, then crochet 2x in the next stitch.

It is so much easier than the way I've been doing it!

AND it is exactly the Algorithm used by the thousands of ladies who have been crocheting Coral Reef Projects for so many years!
See Facebook......I shall get name asap.....




Thus it may be that someone already knows this Pattern is true for the Fibonacci Series   ("egyptian" popped into my mind...  silly....)
I have to understand the underlying Principles for myself.
I must say I astonished myself!

Here is more:-




There is more that I can discuss....sometime later.

The Half Fibonacci Series featured in early work of mine when I was trying to elucidate the Bivalves.

Beginning in 23/6/2010  and also in 26/5/2011,  16/6/2011.    and 12/12/2012,  "responding literally".

Some of my ideas have been mistaken,  but it is all part of the Process of discovering stuff for  myself.

I shall not repeat all the old stuff;  it is there on my blog if anyone wishes to look at it.

Suffice to say,  I hope to be using this new easy method in future work;  enough suffering with difficult Patterns.  I am quite delighted........








And yes,  there may be an entirely different Equation which describes the Patterns of these Numbers; only I haven't finished working on it yet.




















Here is a bit from this blog 26/5/2010  "hyperbolic crochet on  radio"


"Back in August 2009 I managed to catch an interview on ABC Radio National's Artworks program, Amanda Smith chatting with Margaret Wertheim about the Exhibition at Sydney's Powerhouse Museum during Science Week . It was The Sydney Hyperbolic Crochet Reef. Hundreds of people contributed to this colorful show and you can see some of it at http://www.sydneyreef.blogspot.com/
Science meets handicrafts with a view to bring attention to the plight of coral reefs.
When doing craft, time stops.

The algorithm used was " crochet 3 stitches, increase 1 in next stitch. " It's not rigid, you can play with the numbers, to create the shapes of nature."

Then, believe it or not, I caught the moment on radio when Emma Ayres on ABC Classic Breakfast in April gave us the news that Reuters announced the winner of the 2009 Diagram Prize for the Oddest Title for a Book was "Crocheting Adventures with the Hyperbolic Plane" by Dr Daina Taimina. "Splendidly eccentric" said one newspaper, another said "superb juxtaposition...", "the two worlds collide in a captivating and completely breathless way".
and you can see her words on http://www.hyperbolic-crochet.blogspot.com/

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Rummaging around in an Equation.....

Regarding the new Equation announced in the previous post;-
What happens at n = 7,  or if n = 14,  or 15?
What happens at 0,  the singularity?  Do the numbers continue in Series on the "negative" side, as if in another dimension,  maybe the spiritual realm?
We are said to be vibrational Beings,  indeed,  all of Nature could be so.  There was a recent story on Facebook regarding this,  spiritual side of existence.  I might have shared it.


May I leave this for another time, please.
I have another  Post, next,   to bring a Brand New Pattern,
 Algorithm for crocheting and knitting the Fibonacci Series.
Actually it is an old way which I have only just recently been able to understand!

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A New Equation!

You might notice that the Lucas Series figures in the previous algorithm.
2,  1,  3,  4,  7,  11,  18,  29,  47,  76,  ..........exactly or approximately.




Please click on images to enlarge,
to see them more clearly.

















































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Here is the Equation:-






































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There is a lot of work,  calculating it all,    in the series.
How might one interpret it?

I'd like to leave it for another day.  Enough work inputting this data!

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Review of Algorithm 13 to 21 for Fibonacci Series Crochet or Knit Work **

This figuring out began in 2011,  "crafting the vortex",  and the posts following,  of 24th April 2011;  trying to work out how one might evenly increase or decrease the stitches in the rows of this Hyperbolic Shape.
I have been including it in diagram form all along,  giving clues as to how one might do it.
13 stitches to 21 stitches.  There are tables of numbers documenting the figuring out.......

Here in hindsight I can have a go at presenting them fairly simply,  even to the utterly impossible range of thousands of stitches,  as if it were an imaginative task.



















































































































































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Here are the original diagrams......

































-------------------------to be continued.............................

Friday, September 12, 2014

The 144 Model, Crocheted **



 Here is a display of my most recent crochet/knitted seashells.

 None are perfect yet and it's a gruelling business to write up an accurate Pattern.
This page is for writing up the 144 stitch model.  lower right.   Sooner or later.....
There are a number of ways to sew it up.

It's getting better-  lower left shows a new way of using thread=  fine thread crocheted over a thick yarn.  Might help with making thin inner column and thick outer lip=  quite tricky.

The spiral at top of each seashell-  mathematical model uses concentric circles of increasing circumference in accordance with the fibonacci series-----then merged to form spiral ---which is almost exactly right!
There is a lot of maths which I have been figuring out--  will publish when it's documented up.

Also there is such a vast array of configurations to study --- here are some shells I bought in a  Queensland chemist shop for $20.
 (You can see images of others-- Australian Seashore species in a previous post- "Real Seashells",  of 5/4/2013,  courtesy of New Holland Publishers.)






And here is a tiny Australian native snail, found on stem of old zucchini plant last Autumn.   Less than 1 cm long.








to be continued....




Friday, August 22, 2014

The Yellow and White Model **


This continues on from 4/16/2014  "the latest seashell models"





The Mathematics --includes to 144 stitches, as in the yellow and white model.



The result (1)

Oh dear,  it looks a bit funny!   This time the top was stitched close to upper rows instead of to lower down.
Just goes to show what happens when one tries anything.  These models took days and days and days!  Sheer determination just to try to get a Pattern together.  When all of this is done, the Garden might get some attention.  But there is a lot more that's not yet published..........  I only get to electricity and Internet one or two days a week.  A nice motel is where I go;  sometimes to a friend's home,  or to library in town 20 km away from home.

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Later Update    22/8/2014



The result (2):-


 This one looks much better!  It is stitched up quite differently, with a back stitch,   and not so close to the top,  easing down from the very top, padding as we go.

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The same is done with a model which was a disaster back in 19/3/2012 in "On the trail of the fibonacci snail".  It had been impossible to sew up, being too bulky near the tip.
This new way of sewing it up from the tip down works well:-




Therefore the old post is being edited and improved.  It feels good when something better results.
The maths here are for 233 and 144 stitch rows!

The next photo of a real big old seashell has a similar form,  and I look forward to trying to make it.



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Some People and the Models They Make **


I love the snail sculptures made by Mister Finch!

They sure have personality and attitude.

Mister Finch has no problem with making Patterns.  His moths must be made of fur and velvet...

He is on Facebook,  as I am too.
And Selvedge too.

I found the article in Selvedge Magazine of January 2013.....




www.selvedge.org






I have requested permission to use these pics......hope it is ok.




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The  following was found on Dr Ron Knott's famous Fibonacci website,  to do with Maths and Art.  This piece comes from www.woollythoughts.com  by Mathematicians Steve Plummer and Pat Ashforth.  I found it once but am unable to find it again.  I copied it using "control c"  and pasted using "control v",  but the images do not happen here.  You would have to go to original site to see images.

The knitted torus I have seen on Sarah-Marie Belcastro's www.toroidalsnark.net



6. Dual Seven Colored Tori
Carolyn Yackel explains that the dual seven colored tori seen here (one knitted and one crocheted) “implies that a graph on a torus requires at most seven colors in order to color the vertices so that no vertices connected by an edge are the same color.”
7. Crochet Lorenz Manifold
The website for this project explains: “Dr. Hinke Osinga and Professor Bernd Krauskopf have turned the famous Lorenz equations that describe the nature of chaotic systems into a beautiful real-life object, by crocheting computer-generated instructions. Together all the stitches define a complicated surface, called the Lorenz manifold.”
8. Fibonacci Crochet
Many artists use the Fibonacci sequence to create art that is pleasing to the eye. Sculptural textile artist Sophie Buckleyexplored this, shown above, for her final degree show at school.
9. Hyperbolic Crochet Reef Project
There is no way that I could write this article without including the hyperbolic crochet reef project and the various spin-off projects that have come out of that. It was a mathematician who realized that crochet can be used to express hyperbolic math principles that weren’t easily understandable. The Wertheim Sisters, one of whom is an artist and the other a scientist, used these principles to develop the eco-awareness coral reef project, which has grown and grown and been showcased around the world. The image above comes from Helle Jorgensen, an artist who has been greatly inspired by the coral reef project.
There are many other mathematical artists who incorporate hyperbolic crochet into their work, which is not necessarily reefwork. In fact, hyperbolic crochet is probably the most popular type of math based crochet. Consider, for example, this hyperbolic flower blossom by Gabriele Meyer:
10. Variations on Hyperbolic Crochet
Other artists have taken the basic idea of hyperbolic crochet and expanded on it. For example, freelance artist Mickey Shaw-Hubbard says of the hyperbolic mushroom forest shown above: “This crocheted fiber soft sculpture installation is based on non-Euclidean geometry. It represents a variation of the hyperbolic plane ruffle effect.”


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Please also see the work of Dr Daina Taimina who has her own blogspot,  and one called hyperbolic-crochet.  Many of these people are on Facebook.
The Sydney Hyperbolic Crochet Reef  has websites and Facebook too, I think.
The Wertheim Sisters have a website for The Institute for Figuring.

Please see www.knitbitch.blogspot.com  for more crocheted models of many kinds.  I am glad that this website also mentions biomathcraft and has images of some seashells.

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