Here is Figure 2.17

The code shows below:

clear all close all format long % show me lots of digits

%% initialize parameters a = 1.28; b = -0.3; % smooth boundary fig 2.3 a = 1.4; b = -0.3; % fractal boundary fig 2.3 a = 2; b = -0.3; % attractor fig 2.11 a = 0; b = 0.4; % smooth boundary fig 2.9, 2.10 a = 0.43; b = 0.4;

%% initialize plot figure xmin = -2.5; xmax = 2.5; ymin = -2.5; ymax = 2.5; colormap([0 0 0;1 1 1]) axis([xmin xmax -ymax ymax]) fsize=16; fsizea=30; set(gca,'xtick',[xmin:1:xmax],'FontSize',fsize) set(gca,'ytick',[-ymax:1:ymax],'FontSize',fsize) xlabel('x','FontSize',fsizea); ylabel('y','FontSize',fsizea) title('Henon Map','FontSize',fsizea) rect = [0,30,560*1.0,560*0.8]; set(gcf,'Position',rect); set(gcf,'PaperPositionMode','auto');

%% ask for an initial condition disp('Click on a point and press enter'); [x,y] = ginput; disp(sprintf('You chose x = %0.3f, y = %0.3f',x,y)); pause(1) hold on iterates = 100; % how many times we iterate the map lag = 15; % how many iterates are plotted on figure at any time

for j = 1:iterates if mod(j,10) == 0 disp(sprintf('Iterate %s',int2str(j))) end if j == lag disp('Removing Old Iterates') end yold = y; y=x; x=a-x^2+b*yold; % this is the henon map disp(x) h(j)=plot(x,y,'r+','MarkerSize',10); % plot the current orbit point if j > lag delete(h(j-lag)) % remove old iterates end pause(.1) % pause for drama, remove for insane speed end

Use the code henon_iteration.m from the Files tab in the Matlab channel on Teams to recreate figure 2.17. In addition, find and plot a periodic orbit higher than period-16 (panel b). To do so, you'll need to increase the number of iterates performed by the code, as well as the lag parameter specifying how many points are plotted. H + + (a) (b) (c) (d) (e) (f) Use the code henon_iteration.m from the Files tab in the Matlab channel on Teams to recreate figure 2.17. In addition, find and plot a periodic orbit higher than period-16 (panel b). To do so, you'll need to increase the number of iterates performed by the code, as well as the lag parameter specifying how many points are plotted. H + + (a) (b) (c) (d) (e) (f)