How do I make Hanoi graphs using TikZ?

Question

I have a feeling that it is possible to do using tkz-graph, but I don't know how it works. I tried searching for high-resolution images in Google, and no such image showed up.
I need to make the graph with varying n so that the states of the Tower of Hanoi will be evident. A sample of the graph is from WolframAlpha.
Can you help me do it, please?

Don Hosek · Accepted Answer

These are very similar to Sierpinski triangles (just without the fills). I'd start with one of the solutions at How to create a Sierpinski triangle in LaTeX? and make the minor adjustments necessary to get your desired result.

Correct answer by Don Hosek on December 5, 2020

How do I make Hanoi graphs using TikZ?

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