# tf\_mandelbrot\*

Computes the [Mandelbrot set](https://en.wikipedia.org/wiki/Mandelbrot_set) over the complex domain \[`x_min`, `x_max`), \[`y_min`, `y_max`), discretizing the xy-space into an output of dimensions `x_pixels` X `y_pixels`. The output for each cell is the number of iterations needed to escape to infinity, up to and including the specified `max_iterations`.

* [tf\_mandelbrot](/sql/data-manipulation-dml/system-table-functions/tf_mandelbrot#tf_mandelbrot)
* [tf\_mandelbrot\_float](/sql/data-manipulation-dml/system-table-functions/tf_mandelbrot#tf_mandelbrot_cuda)
* [tf\_mandelbrot\_cuda](/sql/data-manipulation-dml/system-table-functions/tf_mandelbrot#tf_mandelbrot_cuda)
* [tf\_mandelbrot\_cuda\_float](/sql/data-manipulation-dml/system-table-functions/tf_mandelbrot#tf_mandelbrot_cuda_float)

## tf\_mandelbrot

```
SELECT * FROM TABLE(
  tf_mandelbrot( 
    x_pixels => <x_pixels>,
    y_pixels => <y_pixels>,
    x_min => <x_min>,
    x_max => <x_max>,
    y_min => <y_min>,
    y_max => <y_max>,
    max_iterations => <max_iterations>
  )
)  
```

| Parameter        | Data Type      |
| ---------------- | -------------- |
| `x_pixels`       | 32-bit integer |
| `y_pixels`       | 32-bit integer |
| `x_min`          | DOUBLE         |
| `x_max`          | DOUBLE         |
| `y_min`          | DOUBLE         |
| `y_max`          | DOUBLE         |
| `max_iterations` | 32-bit integer |

**Example**

![](https://files.buildwithfern.com/heavyai.docs.buildwithfern.com/heavyai/6666a31d1a19bcfcd8c24bad50eba0ea502749a811b0fb7ee897e4117c09c228/docs/assets/heavy_mandelbrot.png)

## tf\_mandelbrot\_cuda

```
SELECT * FROM TABLE(
  tf_mandelbrot_cuda( <x_pixels>, <y_pixels>, <x_min>, <x_max>, <y_min>, <y_max>, <max_iterations>
  )
)
```

<table>
  <thead><tr><th>Parameter</th><th>Data Type</th><th data-hidden>Description</th></tr></thead>

  <tbody><tr><td><code>x_pixels</code></td><td>32-bit integer</td><td /></tr><tr><td><code>y_pixels</code></td><td>32-bit integer</td><td /></tr><tr><td><code>x_min</code></td><td>DOUBLE</td><td /></tr><tr><td><code>x_max</code></td><td>DOUBLE</td><td /></tr><tr><td><code>y_min</code></td><td>DOUBLE</td><td /></tr><tr><td><code>y_max</code></td><td>DOUBLE</td><td /></tr><tr><td><code>max_iterations</code></td><td>32-bit integer</td><td /></tr></tbody>
</table>

## tf\_mandelbrot\_float

```
SELECT * FROM TABLE(
  tf_mandelbrot_float(<x_pixels>, <y_pixels>, <x_min>, <x_max>, <y_min>, <y_max>, <max_iterations>
  )
)
```

<table>
  <thead><tr><th>Parameter</th><th>Data Type</th><th data-hidden>Description</th></tr></thead>

  <tbody><tr><td><code>x_pixels</code></td><td>32-bit integer</td><td /></tr><tr><td><code>y_pixels</code></td><td>32-bit integer</td><td /></tr><tr><td><code>x_min</code></td><td>DOUBLE</td><td /></tr><tr><td><code>x_max</code></td><td>DOUBLE</td><td /></tr><tr><td><code>y_min</code></td><td>DOUBLE</td><td /></tr><tr><td><code>y_max</code></td><td>DOUBLE</td><td /></tr><tr><td><code>max_iterations</code></td><td>32-bit integer</td><td /></tr></tbody>
</table>

## tf\_mandelbrot\_cuda\_float

```
SELECT * FROM TABLE(
  tf_mandelbrot_cuda_float( <x_pixels>, <y_pixels>, <x_min>, <x_max>, <y_min>, <y_max>, <max_iterations>
  )
)
```

<table>
  <thead><tr><th width="260">Parameter</th><th>Data Type</th><th data-hidden>Description</th></tr></thead>

  <tbody><tr><td><code>x_pixels</code></td><td>32-bit integer</td><td /></tr><tr><td><code>y_pixels</code></td><td>32-bit integer</td><td /></tr><tr><td><code>x_min</code></td><td>DOUBLE</td><td /></tr><tr><td><code>x_max</code></td><td>DOUBLE</td><td /></tr><tr><td><code>y_min</code></td><td>DOUBLE</td><td /></tr><tr><td><code>y_max</code></td><td>DOUBLE</td><td /></tr><tr><td><code>max_iterations</code></td><td>32-bit integer</td><td /></tr></tbody>
</table>