Lorenz Equation || Vector lengths should be the same

Hi, im trying to plot the lorenz butterfly using the equations. I can't get past the error "vectors must be of equal length." I understand that this means that one of my vairables has more/lesser points compared to the other two, but I can't figure out how. I can tell you that it is variable z because on plotting 2-D Plot(x,y) works but plot(y,z) and plot(x,z) dont work for the same error. Can someone tell me how to fix this?

This is my code:

x(1) = normrnd(0,1);

y(1) = normrnd(0,1);

z(1) = normrnd(0,1);

sigma= 10;

rho=28;

time = 0.05;

beta= 8/3;

for i = 2:1000

x(i) = x(i-1) + time*sigma*(y(i-1)-x(i-1));

y(i) = y(i-1) + time*(x(i-1)*(rho-z(i-1))-y(i-1));

z(i) = z(i-1) + time*(x(i-1)*y(i-1)-beta*z(i-1));

end

figure

plot3(x,y,z)

Answer 1

[John D'Errico]

First, you need to learn how to preallocate your vectors, and why. That code will be inefficient, because x, y, and z are all being grown dynamically. Yet you know the final size of those arrays will be 1x1000.

help zeros

Now, why does your code fail? We cannot know this, because the code actually works for me. My guess is that one or more of x,y, or z already existed as some unknown size arrays when you ran this code.

What does that mean? When you get an error, LOOK at the variables involved. What size are they? Learn to use whos when you see something confusing.

whos x y z
  Name      Size              Bytes  Class     Attributes

  x         1x1000             8000  double              
  y         1x1000             8000  double              
  z         1x1000             8000  double              

[Hetvi Vora]

okay so I tried that, and this is what I got:

Name Size Bytes Class Attributes

x 1x100000 800000 double

y 1x100000 800000 double

z 1x10000 80000 double

So I'm trying to figure out why z has lesser variables. I'm going to read on preallocating vectors now. I do appreciate all the help you're giving me!

[Hetvi Vora]

okay I fixed this! Yaaay!

But, can you tell me, what output do you get? Is it just a straight line? or do you get the butterfly?

[John D'Errico]

z had a smaller size because x and y and z already existed before. They already had those sizes, probably from different runs that you made.

You may need to get used to starting your scripts with a clear, at least until you learn how to use functions. Best of course is to just get used to knowing what is in your workspace.

Next, for vectors of length 100000, you REALLY need to learn about preallocation. Do this:

x = zeros(1,100000);

for x,y, and z. Now you can assign values to those vectors at will as x(i), with no penalty in speed.

As for the result of that code, I did not actually plot anything. Here is what it produced for me:

x =
  Columns 1 through 11
    -0.063055      0.32584      0.45796      0.73883        1.176       1.8734       2.9819       4.7394       7.5064       11.785       18.094
  Columns 12 through 22
       26.181       31.928       19.221      -39.153       -96.16      -162.81       432.11       6092.8        86594  -3.7605e+07  -1.1072e+11
  Columns 23 through 33
  -3.0645e+17   1.1523e+27   2.5995e+43   1.0172e+69 -1.9466e+111 -6.7249e+178 -9.6366e+288          Inf          NaN          NaN          NaN
  Columns 34 through 44
          NaN          NaN          NaN          NaN          NaN          NaN          NaN          NaN          NaN          NaN          NaN

which is clearly a divergent process. So my guess is you need to check your equations and the parameters you used in them.

[Hetvi Vora]

Thank you so much!

I figured it out with your help and realised that if I adjust the constant to a particular value I get the butterfly - which is what the equation is all about! and I understand now what went wrong.

Thank you again!