// ******************************// *                            *// * "Snowflake" von Koch curve *// *                            *// ******************************clear;clf;// **************// * constants *// **************n = 6;// number of steps // limited to 9 (262 145 points), otherwise the stacksize must be changed// 6 steps (4 097 points) are enough for a good renderingN = 4^n+1; // amount of pointssin_soixante = sqrt(3)/2; // sin(60°)l = 1; // length of the initial line (arbitrary unit)// ******************// * initialisation *// ******************ycourbe = [zeros(1,N)];ycourbe1 = ycourbe;// *************// * functions *// *************function [xx, yy] = etape(x, y)    // from a line [(x(1),y(1)) ; (x(2),y(2))]  // make the line [(xx(1),yy(1)) ; (xx(2),yy(2)) ; (xx(3),yy(3))]  // x and y are 2-cells tables, the ends of the basis line  // xx and yy are 3-cells tables  // the edges of the equilateral triangle    xu = (x(2)-x(1))/3;  yu = (y(2)-y(1))/3;  // third of the basis line vector    xv = 0.5*xu - sin_soixante*yu;  yv = sin_soixante*xu + 0.5*yu;  // vector turned by +60°    xx(1) = x(1)+xu; yy(1) = y(1)+yu;  xx(3) = x(2)-xu; yy(3) = y(2)-yu;    xx(2) = xx(1) + xv;  yy(2) = yy(1) + yv;  endfunctionfunction [xkoch, ykoch] = vonkoch(x, y, n)  // builds the curve  // initialisation  xkoch = x;  ykoch = y;  xkoch1 = x;  ykoch1 = y;  for i=1:n    jmax = 4^(i-1);    // number of lines at the beginning of the step i    for j=1:jmax/2+1      // we work with two points which indices are j and j+1 (line #j)      // thanks t the symmetry, we work with a half curve      decalage = (j-1)*4;       // the new points shift the next points by this offset      x_init = xkoch(j:j+1);      y_init = ykoch(j:j+1);      // line #j      [x_trans, y_trans] = etape(x_init,y_init);      // transformed line      xkoch1(decalage+1) = x_init(1); xkoch1(decalage+5) = x_init(2);      ykoch1(decalage+1) = y_init(1); ykoch1(decalage+5) = y_init(2);      for k=1:3        xkoch1(k+decalage+1) = x_trans(k);        ykoch1(k+decalage+1) = y_trans(k);        // values put in the global vector      end    end    xkoch = xkoch1; ykoch = ykoch1;  end    for i=1:4^n    ykoch(N-i+1) = ykoch(i);    xkoch(N-i+1) = l-xkoch(i);     // 2nd half-curve  endendfunction// ****************// * main program *// ****************xcourbe(2) = l;[xcourbe,ycourbe] = vonkoch(xcourbe,ycourbe,n);// drawing the curvexpoly(xcourbe,ycourbe)isoview(0,l,0,l*sin_soixante/3)

// saving the filename = "von_koch_"+string(n)+"_steps.svg";xs2svg(0, name)

//============================================================================// name: von_koch.sce// author: Christophe Dang Ngoc Chan// date of creation: 2012-10-23// dates of modification: //    2013-07-08: quotes ' -> "//    2013-07-2: vectorisation of the calculations//----------------------------------------------------------------------------// version of Scilab: 5.3.1// required Atoms modules: aucun//----------------------------------------------------------------------------// Objective: draws the von Koch's "snowflake"// Inputs: none (parameters are hard coded)// Outputs: graphical window with a curve; SVG file//============================================================================clear;clf;// *************// * constants *// **************n = 6; // number of steps // limited to 9 (262 145 points), otherwise the stacksize must be changed// 6 steps (4 097 points) are enough for a good renderingsin_soixante = sqrt(3)/2; // sin(60°)l = 1;// length of the initial line (arbitrary unit)// ******************// * initialisation *// ******************// *************// * functions *// *************function [] = vonkoch(A, B, i)    u = (B - A)/3 ; // third of the AB vector    v = [0.5*u(1) - sin_soixante*u(2) ; sin_soixante*u(1) + 0.5*u(2)] ;    // vector turned by +60°    C = A + u ;    D = C + v ;    E = B - u ;    // points of the line    if i == 1 then        // drawing the smallest segments        x = [A(1) ; C(1) ; D(1) ; E(1) ; B(1) ];        y = [A(2) ; C(2) ; D(2) ; E(2) ; B(2) ];        xpoly(x, y, "lines")    else        j = i - 1 ;        vonkoch(A, C, j);        vonkoch(C, D, j);        vonkoch(D, E, j);        vonkoch(E, B, j);        // recursive call    endendfunction// ****************// * main program *// ****************beginning = [0;0] ;ending = [l;0] ;vonkoch(beginning, ending, n)isoview(0,l,0,sin_soixante*l)// Saving the filename = "von_koch_"+string(n)+"_steps.svg" ;xs2svg(0, name)