A little mathematics for Valentine’s day

February 10th, 2010 | Categories: general math | Tags:

This is not a serious post but then mathematics doesn’t have to be serious all the time does it?  Ever wondered what the equation of a 3D heart looks like?  An old post of mine will help you find the answer using Mathematica.  Click on the image for more details (and a demonstration that you can run using the free Mathematica player).

math for yor valentine

I don’t save all of my love for Mathematica though. I’ve got some for MATLAB too:

%code to plot a heart shape in MATLAB
%set up mesh
n=100;
x=linspace(-3,3,n);
y=linspace(-3,3,n);
z=linspace(-3,3,n);
[X,Y,Z]=ndgrid(x,y,z);
%Compute function at every point in mesh
F=320 * ((-X.^2 .* Z.^3 -9.*Y.^2.*Z.^3/80) + (X.^2 + 9.* Y.^2/4 + Z.^2-1).^3);
%generate plot
isosurface(F,0)
view([-67.5 2]);

Did you know that the equation for a heart (or a cardioid if you want to get technical) is very similar to the equation for a flower?  The polar equation you need is  and you get a rotated cardioid for n=1.  Change n to 6 and you get a flower.  Let’s use the free maths package, SAGE, this time.

First, define the function:

def eqn(x,n):
    return(1-sin(n*x))

then plot it for n=1

polar_plot(eqn(x,1), (x,-pi, pi),aspect_ratio=1,axes=False)

SAGE heart
and for n=7

polar_plot(eqn(x,7), (x,-pi, pi),aspect_ratio=1,axes=False)

SAGE heart

Back to Mathematica and the Wolfram Demonstrations project. We have a Valentine’s version of the traditional Tangram puzzle.

Broken Heart Tangram

Feel free to let me know of any other Valentine’s math that you discover, puzzles, fractals or equations, it’s all good :)

Update Feb 14th 2011

Mariano Beguerisse Díaz sent me some MATLAB code that uses a variation on the standard mandelbrot and I turned it into the movie below.  His original code is in the comments section

  1. Mariano
    February 14th, 2011 at 16:55
    Reply | Quote | #1

    I have a ‘fuzzy’ Mandelbrot fractal in MATLAB
    Just run this script, have a go!

    % Fuzzy heart-shaped Mandelbrot fractal
    % Mariano Beguerisse
    % October 2010
    
    % iterations
    n = 300;
    % resolution
    N = 200;
    % Create grid
    x = linspace(-1, 1, N);
    y = linspace(-1.4, .6, N);
    [X,Y] = meshgrid(x, y);
    
    Z = X + i*Y;
    Zn = Z;
    
    figure
    for j=1:n
      % Mandelbrot map with random noise
      Zn = -i*(Zn).^2 +  (rand(N,N).^(1/5)).*Z;
      M = abs(Zn);
      ind1 = find(M<2);
      ind2 = find(M>=2);
      M(ind1) = 0;
      M(ind2) = -1;
      m = 1;
      imagesc(x, y, (M/m)) 
      colormap([1 1 1; 1 0 0])
      set(gca,'YDir','normal')
      title(n-j)
      pause(0.01)
    end
    title('Love or whatever', 'fontsize', 16)
    
    
  2. February 14th, 2011 at 18:06
    Reply | Quote | #2

    That’s nice :)

1 trackbacks

Comments are closed.