Efficient visualisation of arrangements

Question

First, I don't know the word for the set. I have n cases and the set I have is 2^n which lists all their "arrangements" present or absent, so a summation of combinations with k from 0 to n.

Each arrangement has a value and I need to plot this arrangement (in JS with plotly or D3, so anything is doable) but I unsure what graph to use. It's actually an biological problem regarding epistasis, where mutations together are not additive, but may synergise.

My thoughts
The dataset is a square, but that is not visually helpful: the bottom half minus the diagonal of that would be straightforward n-choose-2 combinations (e.g. --++,-+-+), the diagonal n-choose-1 states (---+), while the rest would be higher combinations (-+++), plus the null state (----).
In my code I easily make the display version of the set by iterating through 2^n and converting each index to a binary in string format (i).toString(2).padStart(mutation_number,'0').split("").map((v,i)=>v == "1" ? "+" : "-"). However, a list, e.g. bar chart, seems a terrible way to represent the dataset.
The best I could think is a diamond of lines of circles where each tier i is a the n-choose-i subset. But it would require arrows and may be confusing...

Answer 1

User856 notes that this is called a power set.

I don't think there is a particularly good way to visualize all the elements of a power set as a two-dimensional diagram. A natural geometrical representation is as the vertices of an -dimensional hypercube, but that is hard to draw and harder to interpret.

For my application I ended up using a graph-like representation, where node width represented the value and the user could drag the nodes to avoid confusion. This can be found in epistasis.mutanalyst.com by using the first "demo" data.