[Jprogramming] Explicit fib

Wed Mar 1 18:26:52 UTC 2017

Oh - I don't know how or why it looks like that!   There should be two
single quotes ( ' ),   and no embedded "tie"  ( ` )
Perhaps it's a feature of your mail-handler.
I've noticed that Thunderbird rendered your t caret 3 as t raised-small-3
this morning,  which is not J,  and presumably not what you typed !

In words,

  quote n s quote =. 2 take y, 10

The idea was that s would default to 10 steps per quarter-circle if
the input was a single scalar defining only n,  the number of
Fibonacci elements.

Please do also look at my earlier reply sent 9:30-ish BST,  which attempts
to correct some line-wraps,  corrects a couple of NB. comments and includes
some remarks which might be of some use.

Mike

On 01/03/2017 15:42, Linda A Alvord wrote:
> Mike, I copied but forgot to paste.  Sorry
>
> n`s   =. 2{. y, 10
> |value error: scriptd
> |   n`s=.2{.    y,10
> |[-11] c:\users\user\j64-805-user\temp\fib mike day2.ijs
>     
>
> Linda
>
> -----Original Message-----
> From: Programming [mailto:programming-bounces at forums.jsoftware.com] On Behalf Of Linda A Alvord
> Sent: Wednesday, March 1, 2017 3:19 AM
> To: programming at jsoftware.com
> Subject: Re: [Jprogramming] Explicit fib
>
> Mike,
>
> Here's an error that I am getting.
>
> Linda
>
> -----Original Message-----
> From: Programming [mailto:programming-bounces at forums.jsoftware.com] On Behalf Of 'Mike Day' via Programming
> Sent: Tuesday, February 28, 2017 11:03 AM
> To: programming at jsoftware.com
> Subject: Re: [Jprogramming] Explicit fib
>
> That's the exact approach,  as you know.
>
> Meanwhile,  I'd got the impression that Linda wished to present the
>
> quarter-circle approximations, as shown in, eg,
>
> https://en.wikipedia.org/wiki/Golden_spiral#/media/File:Fibonacci_spiral_34.svg
>
> So I've amused myself for a while developing the following. As each quarter
>
> circle has an offset centre,  I've reverted to Cartesian coords.
>
> It's ended up less transparent than I hoped.  Also,  given the fairly rapid
>
> growth of the Fibonacci sequence,  the later cycles dominate the plot.
>
> (Cliff's reference to his article has just popped up while I was drafting this; it might render all the following redundant!)
>
> NB. Fibonacci spirals:
> NB. radii     1     1    2     3       5     8      13 21       34
> NB. centres (00)  (00) (01) (_1 1) (_1 _1) (2 _1) (2  4) (_6  4)  (_6 _9) NB. differences between centres:
> NB.  diffs     (00) (01) (_1 0) (0 _2)  (3 0)  (0 5)  (_8 0)  (0 _13)
> NB. multipliers needed to derive these differences:
> NB.  mults     (10) (01) (_1 0) (0 _1)  (1 0)  (0 1)  (_1 0)  (0  _1)
>
> mults   =: 1 0 0 1 _1 0 0 _1$~ ,&2
> radii   =: 0 1, fib2"0 @: i. @: -&2    NB. as defined elsewhere in thread
>     NB. Think I'd prefer a vector fib on a scalar input, but no matter, here!
> centres =: +/\@ }:@: (0, radii * mults)
>
> NB. set parameter running over y circles (sets of 2pi) in x steps per quadrant,  from pi/2
> param   =: (] (0.5p1+(2p1 * (#~>:&0))) @: i:@j. (*(8&*)))
>
> xyvals  =: cos,: sin    NB. radius 1, centre 0 0
>
> NB. set up approx Fibonacci Spiral for y[0] circles,  y[1] steps per quadrant spiral  =: 3 : 0
> 'n s'   =. 2{. y, 10
> nt      =. #t       =. s param n
> offsets =. nt{.s#centres 1+4*n     NB. centres in each successive quadrant
> rads    =. nt{.s#}.radii 2+4*n     NB. radii   """"""
> NB. slight inefficiency here, ^^^,  in calling fib2 (or whatever) twice
> xy      =. (|:offsets) + rads *"1 xyvals t   NB. cart coords of quarter
> circles
> ((4*s)%~ i.nt) , xy                NB. return scale (fairly arbitrary)
> with x y coords
> )
>
> 'pensize 2;aspect 1'plot <"1 spiral 2 10       NB. 2-d plot of spiral
>
> 'pensize 2;aspect 1'plot <"1 }. spiral 2 10    NB. 3-d plot of spiral v
> circle counter
>
> I expect it would need simplifying for 10/11 year-olds,  if they're who Linda has in mind.
>
> But a start,  maybe
>
> Mike
>
>
> On 28/02/2017 15:07, Raul Miller wrote:
>> It is begining to sound like you might want this approach:
>>
>> phi=: (1 + %: 5) % 2
>>
>> spiralfib=: verb define
>>      (phi^y) % %:5
>> )
>>
>> fib=: verb define
>>     <. 0.5 + spiralfib y
>> )
>>
>> Is that where you were heading?
>>
>> Thanks,
>>
>
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