{
  "aliases": null,
  "backlinks": [
    {
      "field": "defines",
      "target": "TMY3M75EK8"
    },
    {
      "field": "uses",
      "target": "VXB4G47Z3T"
    }
  ],
  "body": "\n## Summary\n\nAn iterated function system is a finite family of [[contractions|0QN69YA357]] of a complete metric space.\nIt has a unique nonempty compact set, its attractor, that is the union of its images under the maps of the family.\nMany fractals, such as the [[Cantor set|0BXNDZFQME]] and the [[Sierpiński carpet|PCM3H6J3EE]], are attractors of iterated function systems.\nThe attractor can be drawn by applying the maps at random to a point, which is the chaos game.\n\n## Explanations\n\n### L1 human\n\nTake a few rules, each of which shrinks the plane towards some point.\nApply all rules to a picture and put the results together, and repeat.\nWhatever picture you start from, the results converge to one shape, which is made of shrunk copies of itself.\nFor the two rules $x \\mapsto x/3$ and $x \\mapsto x/3 + 2/3$ on the line, the shape is the Cantor set: two copies of itself, each one third as large.\n",
  "commit": "ff8a40749dc16545e3d2fc637f6b0196e81d0bfa",
  "front": {
    "kind": "concept",
    "msc": [
      "28A80",
      "37C70",
      "37H12"
    ],
    "name": "Iterated function system",
    "same_as": {
      "wikidata": "Q1502167",
      "wikipedia": "Iterated function system"
    },
    "sources": [
      {
        "url": "https://en.wikipedia.org/wiki/Iterated_function_system"
      }
    ],
    "tag": "75B8VHDGSA"
  },
  "kind": "concept",
  "link": "https://tamnd.github.io/math2/node/75B8VHDGSA/",
  "links": null,
  "markdown": "https://tamnd.github.io/math2/node/75B8VHDGSA.md",
  "msc": [
    "28A80",
    "37C70",
    "37H12"
  ],
  "name": "Iterated function system",
  "prov": null,
  "role": "",
  "source": "https://github.com/tamnd/math2/blob/main/nodes/75B/75B8VHDGSA.md",
  "status": null,
  "tag": "75B8VHDGSA",
  "uri": "m2://75B8VHDGSA",
  "url": "https://tamnd.github.io/math2/wiki/iterated-function-system/",
  "writing": {
    "tag": "75B8VHDGSA",
    "kind": "concept",
    "level": "W0",
    "next": [
      {
        "what": "an inventory row",
        "note": "the row of the inventory that the node accounts for",
        "have": 0,
        "want": 1
      },
      {
        "what": "a source with a locator",
        "have": 0,
        "want": 1
      }
    ]
  }
}