# Fractal Dimension Index

`D08-F07-A08` · Geometric Chart Patterns → Market Structure, Breakouts, and Regimes · archetype `record-transform` · difficulty 2/5 · verification **verified**

Full page: https://docs.thefintechbuilder.com/geometric-chart-patterns/market-structure-breakouts-and-regimes/fractal-dimension-index/
Agent skill: `npx skills add IslamBaraka90/Fintech-Algorithms-Library` — https://docs.thefintechbuilder.com/guides/agent-skill/

## Install and import

```bash
npm install fintech-algorithms
```

```ts
import { fractalDimensionIndex } from "fintech-algorithms/geometric-chart-patterns/market-structure-breakouts-and-regimes/fractal-dimension-index";
```

## Signature

```ts
fractalDimensionIndex(input)
```

Compares the total path length walked by close over a window against the straight-line span of that window, on a log scale, and clamps the result to [1, 2]. Near 1 the path is a line; near 2 it fills the range.

## Parameters

| Name | Type | Required | Notes |
| --- | --- | --- | --- |
| `input` | `TopicInput` | yes | `bars` is the required OHLCV history, strictly ordered by `timestamp` and on a single adjustment basis. `parameters.period` (default `20`, integer of at least 2) sets the window and is also the log base of the normalisation. |

## Returns

`TopicResult`

`series` and `latest` carry a single `value` key, always between 1 and 2. The warm-up is `period` bars, so with the default `ready_at` is 20; a window with zero path length or zero span yields exactly 1 rather than a null.

## Warm-up

The first `period bars (20 by default)` positions are `null`. The window spans indices i-period through i inclusive - `period + 1` closes - so the first computable index is `period`.

## Errors

- When `period` is supplied as a non-integer or as a value below 2 — throws Error
- When a bar's `close` is not a finite number — throws Error

## Complexity

Time `O(n × period)`, space `O(n)`.

## Worked example

Captured by running this function on the input its own test provides. Real output of real code — but not asserted against a published figure.

### Input

`input`:

```json
{
  "bars": [
    {
      "timestamp": "2024-01-02",
      "basis": "synthetic-unadjusted",
      "open": 100,
      "high": 101.45,
      "low": 98.695,
      "close": 100,
      "volume": 750000,
      "benchmark": 200
    },
    {
      "timestamp": "2024-01-03",
      "basis": "synthetic-unadjusted",
      "open": 101.49111452,
      "high": 103.38381693,
      "low": 100.05480022,
      "close": 101.78791214,
      "volume": 795117,
      "benchmark": 200.56326135
    },
    {
      "timestamp": "2024-01-04",
      "basis": "synthetic-unadjusted",
      "open": 102.45519048,
      "high": 104.6701838,
      "low": 100.91147007,
      "close": 102.9549389,
      "volume": 840234,
      "benchmark": 201.11020913
    }
  ],
  "parameters": {}
}
```

### Call

```ts
fractalDimensionIndex(input)
```

### Returns

object with 9 fields: topic_id, title, state, ready, ready_at, series, latest, parameters, …

```json
{
  "topic_id": "D08-F07-A08",
  "title": "Fractal Dimension Index",
  "state": "calculated",
  "ready": true,
  "ready_at": 20,
  "series": {
    "value": [null, null, null, null, null, null]
  },
  "latest": {
    "value": 1.209221037242474
  },
  "parameters": {},
  "diagnostics": {
    "causal": true,
    "input_count": 96
  }
}
```

## Verification and provenance

Tier: **verified** (via E).

The worked example below is the figure published in this algorithm's article, replayed and asserted by the test suite on every build. The arithmetic cannot drift without the build failing.

Both tiers guarantee the signature. Full explanation: https://docs.thefintechbuilder.com/guides/verification/

Generated from the docs.json payload shipped inside fintech-algorithms@0.13.0.
The signature and parameter list are checked against the compiled implementation at build time,
so a description that contradicts the code fails the build rather than reaching this file.

## Links

- Article (how it works, step by step): https://thefintechbuilder.com/geometric-chart-patterns/market-structure-breakouts-and-regimes/fractal-dimension-index/
- Implementation source: https://github.com/IslamBaraka90/Fintech-Algorithms-Library/blob/main/src/geometric-chart-patterns/market-structure-breakouts-and-regimes/fractal-dimension-index/impl.ts
- Package on npm: https://www.npmjs.com/package/fintech-algorithms
- Domain index for agents: https://docs.thefintechbuilder.com/geometric-chart-patterns/llms.txt