Doesn't have the fancy d3 visualization, but here's a better analysis over the long run (30 years). It even stacks the deck against owning at the start by assuming 100% financing. There's a few missing components (mortgage insurance etc.) but even if you add those numbers into this rather detailed analysis, the conclusion doesn't change. It's actually a good enough analysis that you can just added or subtract a few other scenarios from it yourself and until you're describing some very bizarre circumstances, the basic conclusion holds. All the calculations and reasoning are provided here. Buying is unambiguously a better use of your money over the long term. It's not even close.
http://assayviaessay.blogspot.com/2014/04/rent-or-buy.html
Lots of people here describe renting as having an upside because you can remain location mobile, but that's true of owning as well. The only option at that point isn't to sell your home and then buy one somewhere else, you can also rent out your current home, and buy a second one. You can continue doing that ad nauseum, except now you've convinced other people to pay for your mortgage instead of you. In the end you'll own a few properties and all the people who rented from you will own nothing.
Something mentioned in my link but not explicitly in the OP, rent goes up, mortgage payments stay the same or can go down. Over 30 years, your housing burden goes down significantly providing you with increased monthly liquidity.
At the end of the day, you own the property at the end and for all years >30 you effectively live for "free" (minus taxes).
I urge everybody reading the OP to take a few spare hours and run the numbers themselves and see if the easy conclusion here holds out for them.