Hi everyone,

My brother and I were discussing the Fibonacci sequence yesterday when 
my brother discovered patterns showing up when dividing current and last 
numbers in the sequence. As it turns out, this is one way to calculate 
the golden ratio. Many of you already know this, but I still think it's 
really neat :)

Anyway, it was the Fibonacci sequence which got me to looking up other 
things, and I once again found the page for Penrose tiling. Only this 
time, I was able to understand some of what was being described, hence 
this image :) And wouldn't you know it, the golden ratio came in handy 
for most aspects of it!

I was a fun exercise :D

Sam

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Preview of image 'penrosedeflation15_27.jpg'

Just in case you're interested, here's the same set with the curved 
areas colored in~

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Attachments:
Download 'penrosedeflationb.png' (128 KB)

Preview of image 'penrosedeflationb.png'

stbenge <UN### [at] hotmailcom> wrote:
> Hi everyone,
>
> My brother and I were discussing the Fibonacci sequence yesterday when
> my brother discovered patterns showing up when dividing current and last
> numbers in the sequence. As it turns out, this is one way to calculate
> the golden ratio. Many of you already know this, but I still think it's
> really neat :)
>
> Anyway, it was the Fibonacci sequence which got me to looking up other
> things, and I once again found the page for Penrose tiling. Only this
> time, I was able to understand some of what was being described, hence
> this image :) And wouldn't you know it, the golden ratio came in handy
> for most aspects of it!
>
> I was a fun exercise :D
>
> Sam

A really fun exercise for you, a new world to explore for me...
Thanks Sam!
:-)

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Carlo C. wrote:
> stbenge <UN### [at] hotmailcom> wrote:
>> I was a fun exercise :D
>>
> A really fun exercise for you, a new world to explore for me...
> Thanks Sam!
> :-)

Thanks! You're welcome :)

I'm thinking about trying a version with seven-fold symmetry, if I can 
just figure it out :S

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As usual an interesting and pictorial solution for your fun exercises!
;-)
Paolo

 >stbenge  on date 31/10/2009 03:29 wrote:
> Hi everyone,
> 
> My brother and I were discussing the Fibonacci sequence yesterday when 
> my brother discovered patterns showing up when dividing current and last 
> numbers in the sequence. As it turns out, this is one way to calculate 
> the golden ratio. Many of you already know this, but I still think it's 
> really neat :)
> 
> Anyway, it was the Fibonacci sequence which got me to looking up other 
> things, and I once again found the page for Penrose tiling. Only this 
> time, I was able to understand some of what was being described, hence 
> this image :) And wouldn't you know it, the golden ratio came in handy 
> for most aspects of it!
> 
> I was a fun exercise :D
> 
> Sam
> 
> ------------------------------------------------------------------------
>

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Paolo Gibellini wrote:
> As usual an interesting and pictorial solution for your fun exercises!
> ;-)
> Paolo

Thanks!

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On 1-11-2009 21:10, stbenge wrote:
> Carlo C. wrote:
>> stbenge <UN### [at] hotmailcom> wrote:
>>> I was a fun exercise :D
>>>
>> A really fun exercise for you, a new world to explore for me...
>> Thanks Sam!
>> :-)
> 
> Thanks! You're welcome :)
> 
> I'm thinking about trying a version with seven-fold symmetry, if I can 
> just figure it out :S

If it was easy Penrose would have found and patented it.

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