MAKE A MEME
View Large Image
| View Original: | Amoeba4 400.png (1896x1917) | |||
| Download: | Original | Medium | Small | Thumb |
| Courtesy of: | commons.wikimedia.org | More Like This | ||
| Keywords: Amoeba4 400.png Made by myself with Matlab Source code MATLAB <source lang Matlab > find the amoeba of the polynomial p z w 50 z 3+83 z 2 w+24 z w 2+w 3+392 z 2+414 z w+50 w 2-28 z +59 w-100 See http //en wikipedia org/wiki/Amoeba_ mathematics function main figure 3 ; clf; hold on; axis equal; axis off; axis -4 5 5 -3 5 6 ; fs 20; set gca 'fontsize' fs ; ii sqrt -1 ; tiny 100 eps; Ntheta 500; for Ntheta 500 the code will run very slowly but will get a good resolution NR Ntheta; R is a vector of numbers exponentiall distributed A -5; B 5; LogR linspace A B NR ; R exp LogR ; a vector of angles uniformly distributed Theta linspace 0 2 pi Ntheta ; degree 3; Rho zeros 1 degree Ntheta ; Rho will store the absolute values of the roots One ones 1 degree Ntheta ; play around with these numbers to get various amoebas b1 1; c1 1; b2 3; c2 15; b3 20; c3 b3/5; d -80; e d/4; f 0; g 0; h 20; k 30; l 60; m 0; n -10; p 0; q 0; Draw the 2D figure as union of horizontal slices and then union of vertical slices The resulting picture achieves much higher resolution than any of the two individually for type 1 2 for count_r 1 NR count_r r R count_r ; for count_t 1 Ntheta theta Theta count_t ; if type 1 z r exp ii theta ; write p z w as a polynomial in w with coefficients polynomials in z first comes the coeff of the highest power of w then of the lower one etc Coeffs 1+m c1+c2+c3+b1 z+b2 z+b3 z+k+p z e+g+ c1+b1 z c2+b2 z + c1+c2+b1 z+b2 z c3+b3 z +l z+q z 2 d+f z+ c3+b3 z e+ c1+b1 z c2+b2 z +h z 2+n z 3; else write p z w as a polynomial in z with coefficients polynomials in w w r exp ii theta ; Coeffs b1 b2 b3+n h+b1 b3 c2+w +b2 b3 c1+w +b1 c3+w +q w b2 c1+b1 c2 c3+b3 c1 c2+e +f+ b1 c2+b3 c1+c2 +b1 c3+b2 c1+c3 +l w+ b1+b2+b3 w 2+p w 2 d+c3 c1 c2+e + c1 c2+ c1+c2 c3+e+g w+ c1+c2+c3+k w 2+w 3+m w 3; end find the roots of the polynomial with given coefficients Roots roots Coeffs ; log root Use max to avoid log 0 Rho degree count_t-1 +1 degree count_t log max abs Roots tiny ; end plot the roots horizontally or vertically if type 1 plot LogR count_r One Rho 'b ' ; else plot Rho LogR count_r One 'b ' ; end end end saveas gcf sprintf 'amoeba4_ d eps' NR 'psc2' ; </source> derivative works Amoeba4 400 svg amoeba mathematics Images with Matlab source code Files by User Oleg Alexandrov from en wikipedia math | ||||
