Batman equation in MATLAB

Hi folks,

I am looking for a smart way to implement the Batman equation in MATLAB:

http://www.freepostia.com/fimages/405CNy9J_image.jpg

I came up with this:

syms x y

eq1 = ((x/7)^2*sqrt(abs(abs(x)-3)/(abs(x)-3))+(y/3)^2*sqrt(abs(y+3/7*sqrt(33))/(y+3/7*sqrt(33)))-1);
eq2 = (abs(x/2)-((3*sqrt(33)-7)/112)*x^2-3+sqrt(1-(abs(abs(x)-2)-1)^2)-y);
eq3 = (9*sqrt(abs((abs(x)-1)*(abs(x)-.75))/((1-abs(x))*(abs(x)-.75)))-8*abs(x)-y);
eq4 = (3*abs(x)+.75*sqrt(abs((abs(x)-.75)*(abs(x)-.5))/((.75-abs(x))*(abs(x)-.5)))-y);
eq5 = (2.25*sqrt(abs((x-.5)*(x+.5))/((.5-x)*(.5+x)))-y);
eq6 = (6*sqrt(10)/7+(1.5-.5*abs(x))*sqrt(abs(abs(x)-1)/(abs(x)-1))-(6*sqrt(10)/14)*sqrt(4-(abs(x)-1)^2)-y);

axes('Xlim', [-7.25 7.25], 'Ylim', [-5 5]);
hold on

ezplot(eq1,[-8 8 -3*sqrt(33)/7 6-4*sqrt(33)/7]);
ezplot(eq2,[-4 4]);
ezplot(eq3,[-1 -0.75 -5 5]);
ezplot(eq3,[0.75 1 -5 5]);
ezplot(eq4,[-0.75 0.75 2.25 5]);
ezplot(eq5,[-0.5 0.5 -5 5]);
ezplot(eq6,[-3 -1 -5 5]);
ezplot(eq6,[1 3 -5 5]);
colormap([0 0 1])

title('Batman');
xlabel('');
ylabel('');
hold off

Any other ideas are welcome.

[Oleg Komarov]

I've submitted just less than a week ago the BATMAN equation to Martin Sona's question but he apparently deleted it (so much of my time...but cache is good)

Answer 1

[Oleg Komarov]

The "correct" version with explanations: http://math.stackexchange.com/questions/54506/is-this-batman-equation-for-real

% Grey axes

    axes('Xlim'  ,[-7 7]    , 'Xtick' ,-7:7,...
         'Ylim'  ,[-5 5]    , 'Ytick' ,-5:5,...
         'YtickL',''        , 'XtickL',''  ,...
         'Ygrid' ,'on'      , 'Xgrid' ,'on',...
         'Xcolor',[.8 .8 .8], 'Ycolor',[.8 .8 .8]);
    hold on

% Outer wings

    f1 = '(x/7)^2 * sqrt(abs(abs(x)-3)/(abs(x)-3)) + (y/3)^2 * sqrt(abs(y + 3/7*sqrt(33))/(y + 3/7*sqrt(33))) - 1';
    ezplot(f1,[-8 8 -3*sqrt(33)/7 6-4*sqrt(33)/7]);

% Bottom

    f2 = 'abs(x/2)-(3*sqrt(33)-7) * x^2/112 - 3 + sqrt(1-(abs(abs(x)-2)-1)^2) - y';
    ezplot(f2,[-4 4]);

% Outer ears

    f3 = '9 * sqrt(abs((1-abs(x))*(abs(x)-0.75)) / ((1-abs(x))*(abs(x)-0.75))) - 8*abs(x) - y';
    ezplot(f3,[-1    -0.75 -5 5]);
    ezplot(f3,[ 0.75  1    -5 5]);

% Inner ears

    f4 = '3*abs(x) + 0.75*sqrt(abs((0.75-abs(x))*(abs(x)-.5)) / ((.75-abs(x))*(abs(x)-.5))) - y';
    ezplot(f4,[-0.75 0.75 2.25 5]);

% Connect inner ears (flat line)

    f5 = '2.25*sqrt(abs(((0.5-x)*(0.5+x))/((0.5-x)*(0.5+x)))) - y';
    ezplot(f5,[-0.5 0.5 -5 5]);

% Inner wings

    f6 = '6*sqrt(10)/7 + (1.5-0.5*abs(x)) * sqrt(abs(abs(x)-1) / (abs(x)-1)) - 6*sqrt(10)/14 * sqrt(4-(abs(x)-1)^2) - y';
    ezplot(f6,[-3 -1 -5 5]);
  ezplot(f6,[ 1  3 -5 5]);

% Change line color and width

    set(get(gca,'children'),'Color','b','Linew',2)

% Title and labels

    title('Batman'); xlabel(''); ylabel('')

% Superimpose black axes with xy-ticklabels

    xlbl(1:15,1:2) = ' '; xlbl([1,8,15],:) = ['-7';' 0';' 7'];
    ylbl(1:11,1:2) = ' '; ylbl([1,6,11],:) = ['-5';' 0';' 5'];

    axes('Xlim'  ,[-7 7], 'Xtick' ,-7:7,...
         'Ylim'  ,[-5 5], 'Ytick' ,-5:5,...
         'YtickL',ylbl  , 'XtickL',xlbl,...
         'Box'   ,'on'  , 'Color' ,'none');

*EDIT*

The link shows that all the f# are multiplied and plotted but it doesn't work because ezplot somehow plots the real part of the imaginary numbers(?).

With the piecewise implementation only the core functions should be used (but I left the extended version so that others can copy):

    f1 = '(x/7)^2 + (y/3)^2 - 1';
    f2 = 'abs(x/2)-(3*sqrt(33)-7) * x^2/112 - 3 + sqrt(1-(abs(abs(x)-2)-1)^2) - y';
    f3 = '9  - 8*abs(x) - y';
    f4 = '3*abs(x) + 0.75 - y';
    f5 = '2.25 + 0*x - y';
    f6 = '6*sqrt(10)/7 + (1.5-0.5*abs(x)) - 6*sqrt(10)/14 * sqrt(4-(abs(x)-1)^2) - y';

The result:

[Friedrich]

Nice one :)

How did you post a picture here?

[Oleg Komarov]

Upload it somewhere and then post the link included in <<http://...>>

There's a post on fex which is a collection of repositories.

[Walter Roberson]

The post listing a partial list of repositories is http://www.mathworks.com/matlabcentral/answers/7924-where-can-i-upload-images-and-files-for-use-on-matlab-answers

Answer 2

[Sally Al Khamees]

Starting MATLAB R2016b, you may use fimplicit function to plot the equations.Note that I used the Symbolic Math Toolbox to create the symbolic variables x and y.

You can read more about fimplicit here https://www.mathworks.com/help/matlab/ref/fimplicit.html

syms x y
eq1 = ((x/7)^2*sqrt(abs(abs(x)-3)/(abs(x)-3))+(y/3)^2*sqrt(abs(y+3/7*sqrt(33))/(y+3/7*sqrt(33)))-1);
eq2 = (abs(x/2)-((3*sqrt(33)-7)/112)*x^2-3+sqrt(1-(abs(abs(x)-2)-1)^2)-y);
eq3 = (9*sqrt(abs((abs(x)-1)*(abs(x)-.75))/((1-abs(x))*(abs(x)-.75)))-8*abs(x)-y);
eq4 = (3*abs(x)+.75*sqrt(abs((abs(x)-.75)*(abs(x)-.5))/((.75-abs(x))*(abs(x)-.5)))-y);
eq5 = (2.25*sqrt(abs((x-.5)*(x+.5))/((.5-x)*(.5+x)))-y);
eq6 = (6*sqrt(10)/7+(1.5-.5*abs(x))*sqrt(abs(abs(x)-1)/(abs(x)-1))-(6*sqrt(10)/14)*sqrt(4-(abs(x)-1)^2)-y);
fimplicit([eq1, eq2, eq3, eq4, eq5, eq6],'Color','black','Linew',2)
xlim( [-7.25 7.25])
ylim([-5 5])
grid

[Jonas57]

Very Nice! :D

[Sama Elsayed]

how can I make the batman sign a moving plot? like make it plot instead of just popping up when code is evaluted?

Answer 3

[Jan]

See https://www.mathworks.com/matlabcentral/fileexchange/33124-batman-equation--the-legend