Creating a bracketology background vector art can be achieved using React ART. Here's a brief snippet to get you started:

import React from 'react';
import { SVG } from 'react-art';

const bracketArt = () => {
  return (
    <SVG
      width={400}
      height={600}
      data={require('./bracketArt.json')}
    />
  );
};

export default bracketArt;

In this example, we're using the react-art library to render a vector graphic. The data prop is set to a JSON file containing the bracket art design.

You'll need to create a bracketArt.json file with the following structure:

{
  "glyphs": [
    {
      "x": 10,
      "y": 10,
      "width": 50,
      "height": 50,
      "d": "M 20 20 L 30 30 L 40 40 Z"
    },
    // Add more glyphs here
  ]
}

This is just a basic example to get you started. You can customize the design and add more features as needed.

Note: Make sure to install react-art and @expo/vector-icons in your project using npm or yarn before running this code.