Why do I keep getting back 'Error using zeros' when I run my script?

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Mark Dillon 2015-7-16

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Each time I run my script I get this:

Error using zeros
Maximum variable size allowed by the program is exceeded.
Error in HW3_2 (line 9)
x = zeros(1:50001);

Here is the script I am running:

%%Fractal Curves / Chaos Game / Dragon Curve
% Initially x=0 and y=1, then goes through 50k iterations 
x = zeros(1:50001);
y = ones(1:50001);
% Randi - Uniformly distributed pseudorandom integers
    % For example:
    % X=randi(max) returns a pseudorandom scalar integer between 1 and max.
% Rules
    % 1: x(n+1)=(x(n)-y(n))/4 - (1/2) and y(n+1)=(x(n)+y(n))/4 + 1
    % 2: x(n+1)=(y(n)-x(n))/4 + (1/2) and y(n+1)=-(y(n)+x(n))/4 + 1
    % 3: x(n+1)=(x(n)+y(n))/2 + 1 and y(n+1)=(y(n)-x(n))/2
%%Finding values for x and y
for k = 1:length(x)-1
    rule = randi(3); % See definition above in line 12-14
    if rule == 1
        x(k+1)=(x(k)-y(k))/4 - (1/2);
        y(k+1)=(x(k)+y(k))/4 + 1;
    elseif rule == 2
        x(k+1)=(y(k)-x(k))/4 + (1/2);
        y(k+1)=-(y(k)+x(k))/4 + 1;
    elseif rule == 3
        x(k+1)=(x(k)+y(k))/2;
        y(k+1)=(y(k)-x(k))/2;
    end
end
plot(x,y,'.r');
title('Partial Boundary of Dragon Curve');