Create a function to generate and plot the Sierpinski's triangle with side length $1$ and user$-$defined iteration numbers. Define your function output and name as

$[x,y]=$ sierpinski$(N)$

where $N$ is the number of iterations. $x,y$ are the output of your function, which are the $x$ and $y$ coordinates of the scattered points forming the triangular shapes.

In your function, first, create $x$ and $y$ zeros vectors of the length $N.$

Second, use for$-$loop to iterate from $2$ to $N,$ and generate a random number from $\{0,1,2\}$ and assign it to variable $c$ at the beginning of each step.

Third, in each step, implement the switch$-$case statements. Use the variable $c$ as the switch expression, and use integer $0,1$ and $2$ as case expressions.

$In$ case $0,dox(i)=0\mathrm{.}5*x(i-1)$;$y(i)=0\mathrm{.}5*y(i-1).$

$In$ case $1,dox(i)=0\mathrm{.}5*x(i-1)+0\mathrm{.}25$;$y(i)=0\mathrm{.}5*y(i-1)+\frac{\sqrt[\phantom{2}]{3}}{4.}$

$In$ case $2,dox(i)=0\mathrm{.}5*x(i-1)+0\mathrm{.}5$;$y(i)=0\mathrm{.}5*y(i-1).$

Last but not least, plot your $x$ and y vectors to obtain the Sierpinski's triangle similar to the following illustration.