Please provide matlab or python code and visual of output.

Arnold's cat map is define on the torus by the matrix $A=([2,1],[1,1]).$ The torus is the plane in which two points $(x_1,y_1)$ and $(x_2,y_2)$ are identified if $x_1-x_2$ and $y_1-y_2$ are integers. Alternatively, we can define it as a map on the square $\{(x,y)$: by the formula

$f(x,y)=(frac(2x+y),$frac$(x+y))$

where frac$(x)$ is the fractional part of $x,$ i$.$e$.,$ frac$(x)=x-{|}_{{?}_{?}}{x}_{{?}_{?}}|$ for ${|}_{{?}_{?}}{x}_{{?}_{?}}|$ is the smallest integer not less than $x($it is implemented in Matlab$).$

Draw the circle with center in $(\frac{1}{2},\frac{1}{2})$ with radius $\frac{1}{4}$ and apply $f$ to it repeatedly. Plot first $10$ results.