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| Keywords: Conformal map.svg Illustration of a conformal map self-made with MATLAB tweaked in Inkscape 03 38 23 January 2008 UTC Oleg Alexandrov Source code MATLAB <source lang matlab > Compute the image of a rectangular grid under a a conformal map function main N 15; num of grid points epsilon 0 1; displacement for each small diffeomorphism num_comp 10; number of times the diffeomorphism is composed with itself S linspace -1 1 N ; X Y meshgrid S ; graphing settings lw 1 0; KSmrq's colors red 0 867 0 06 0 14; blue 0 129 205/256; green 0 200 70/256; yellow 254 194 0/256; white 0 99 1 1 1; mycolor blue; start plotting figno 1; figure figno ; clf; shiftx 0; shifty 0; scale 1; do_plot X Y lw figno mycolor shiftx shifty scale I sqrt -1 ; Z X+I Y; tweak these numbers for a pretty map z0 1+ 2 I; z1 0 1+ 0 2 I; z2 0 2+ 0 3 I; a 0 01; b 0 02; shiftx 0 1; shifty 1 2; scale 1 4; F Z+z0 2 +a Z+z1 3 +b Z+z2 4; F 1+2 I F; XF real F ; YF imag F ; do_plot XF YF lw figno mycolor shiftx shifty scale axis -1 1 3 -2 2 ; axis off; saveas gcf 'Conformal_map eps' 'psc2' ; function do_plot X Y lw figno mycolor shiftx shifty scale figure figno ; hold on; M N size X ; X X - min min X ; Y Y - min min Y ; a max max max abs X max max abs Y ; X X/a; Y Y/a; X scale X-shiftx ; Y scale Y-shifty ; for i 1 N plot X i Y i 'linewidth' lw 'color' mycolor ; plot X i Y i 'linewidth' lw 'color' mycolor ; end axis -1-small 1+small -1-small 1+small ; axis equal; axis off; </source> diffeomorphisms Complex analysis Conformal mapping Files by User Oleg Alexandrov from en wikipedia Images with Matlab source code | ||||
