namely? I do see there were some problems in the display of verb "spiral" (despite pasting the stuff to a text notepad file and then copying/ pasting into Thunderbird! - sorry again)
I've attempted some inline edits below. Maybe they'll work... Also, I see I'd swapped the comments on the 2-d and 3-d plot examples! I've just now thought of Googling "Fibonacci Helix" which revealed the idea of drawing cylindrical quarter-spirals in successive nested cubes of size 1 1 2 3 5... Needs a bit of work! You mentioned just now trying: 'pensize 2;aspect 1'plot ((t^3)*sin t);(t^3)*cos t=:do 0,(o.4.5),100 but that suggests you should give Raul's proposal a shot, something like 'pensize 2;aspect 1'plot [t;] ((phi^t)*sin t);(phi^t)*cos t (ie with or without t; ^^^^ NOT J notation! ) It seems a lot simpler to draw the exact helix in some such fashion, than to develop the fractal squares or cubes that I'd started on. Mike On 01/03/2017 08:18, Linda A Alvord wrote:
Mike, Here's an error that I am getting. Linda -----Original Message----- From: Programming [mailto:programming-boun...@forums.jsoftware.com] On Behalf Of 'Mike Day' via Programming Sent: Tuesday, February 28, 2017 11:03 AM To: programm...@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 NB. circles ((4*s)%~ i.nt) , xy NB. return scale (fairly arbitrary) NB. with x y coords ) 'pensize 2;aspect 1'plot <"1 spiral 2 10 NB. 3-d plot of spiral v NB. circle counter 'pensize 2;aspect 1'plot <"1 }. spiral 2 10 NB. 2-d plot of spiral 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,--- This email has been checked for viruses by Avast antivirus software. https://www.avast.com/antivirus ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm ---------------------------------------------------------------------- For information about J forums see http://www.jsoftware.com/forums.htm
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