Visually Showing Binomial Becomes Similar to Poisson

Hi there!

I would like to run the following simple experiment to show that a binomial random variable becomes very similar to a Poisson random variable.

(1) Start with a random variable X that is binomial with parameters (n,p): this can be user-input or randomly chosen within prespecified bounds.

(2) Visually show the distribution of this initial distribution.

(3) Increase n to a specified number.

(4) Visually show how the distribution changes as n increases.

(5) Compare the final distribution from (4) with a Poisson distribution with arrival rate np.

(6) Do similar with a decrease of p and repeat (3)-(5) steps.

(7) Do similar with an increase of n and decrease of p at the same time and repeat (3)-(5).

My challenge is with (3)-(4). I am OK with just defining a random variable, but how can I keep track of the change of its distribution change as the parameter of interest changes? I looked at this article (https://www.mathworks.com/help/stats/probabilitydistributionfunction-app.html), but I want the distribution function to change its shape from the starting value, say n=5, to the end value, say n=100, and visualize the change. Do I use disttool?

As you noticed, I am trying to construct Poisson distribution by starting off with a low-probability coin and tossing extremely fast. (enlarge n, reduce p)

Thanks in advance!