NB. Cauchy Curve Examples NB. J Script, September 2008 NB. William R. Jones & Cliff Reiter NB. Run in small selections to see NB. all the samples require 'plot' NB. path to save images if desired NB. pathf=:'c:\temp\' NB. utilities and addon require 'plot bmp' require '~addons/media/image3/prevare.ijs' NB. save plot utility splot=:3 : 0 pd 'save bmp c:\temp\temp.bmp 720 720' b=.readbmp 'c:\temp\temp.bmp' (256 256 256#:b)write_image y ) NB. complex parametrization of unit circle r=: ^@j. r steps 0 2p1 3 $C=:r steps 0 2p1 10000 cplot=: 'Aspect 1;pensize 2'&plot cplot C NB. splot pathf,'fig01.png' NB. differences approx differential diff=: }. - }: mdpt=: [: -: }. + }: f=:1 + 3 * ^&3 +/(f mdpt C) * diff C cplot +/\(f mdpt C) * diff C NB. CAUchycuRVE chycu=:1 : 0 0,+/\(u mdpt y) * diff y : x&u chycu y ) NB. plot cauchy curve cplot f chycu C NB. splot pathf,'fig02.png' NB. cauchy curve and magnitude cplot ^&5 chycu C cmplot=: 1 : 0 z=.u chycu y opts=.'pensize 2;aspect 1;penstyle 0 1' opts plot z,:(|z)r. 12 o.y ) NB. see dashes with fewer points ^&5 cmplot sC=:r steps 0 2p1 200 NB. splot pathf,'fig03.png' (1+9*^&8) cmplot sC NB. splot pathf,'fig04.png' NB. rational functions f=:1 0 0 0 0 0 2&p.%1.01+^&12 lC=:r steps 0 2p1 30000 cplot f chycu lC NB. splot pathf,'fig05.png' NB. plots cauchy path for all x&u NB. show a family cfplot=:1 : 0 : opts=.'pensize 2;aspect 1;itemcolor ' opts=.opts,":,Hue steps 0 2r3 ,#x opts plot x u chycu"_1 _ y ) NB. circles (2+i.11) (]^[) cfplot C NB. splot pathf,'fig06.png' NB. heart family fh6=:1 0 0 0 0 0 2&p.@] % 1.01+]^[ lC=:r steps 0 2p1 30000 ({.,{:)a=: 12*1.07^ steps 0 0.36 100 a fh6 cfplot lC NB. splot pathf,'fig07.png' NB. cos family ({.,{:) a=: 4*0.9^steps 0 1 50 a cos@:([**:@]) cfplot C NB. splot pathf,'fig08.png' NB. alternate initial paths NB. pp: point to point adverb pp=: 2 : '(m&*@-.+n&*)@(1&|)' ss=: _1j_1 pp 1j_1 ee=: 1j_1 pp 1j1 nn=: 1j1 pp _1j1 ww=: _1j1 pp _1j_1 NB. rsq: complex para of +-1 square rsq=:ss`ee`nn`ww@.(4|<.)"0 sq=: rsq steps 0 4 50000 (2+i.11) (]^[) cfplot sq NB. splot pathf,'fig09.png' $ell=:(cos j. 0.9 * sin)steps 0 2p1 30000 (12*1.07^ steps 0 0.5 100) fh6 cfplot ell NB. splot pathf,'fig10.png' NB. 3 mk_html_gallery _320 _280 images_in pathf