﻿ heatmap – Algosim documentation
Algosim documentation: heatmap

# heatmap

Creates a heat map plot of a scalar field.

## Syntax

• `heatmap(f, ❨xmin, xmax[, δx]❩, ❨ymin, ymax[, δy]❩[, c[, m]])`

• `f` is a function D → ℝ where D ⊂ ℝ²

• `xmin`, `xmax`, `ymin`, and `ymax` are real numbers

• `δx` and `δy` are non-negative real numbers

• `c` is a colour, a list of two or three colours, or a function [0, 1] → colours

• `m` is a boolean

## Description

The `heatmap` function creates a heat map plot of the scalar field `f` in the rectangular region `[xmin, xmax] × [ymin, ymax]` with a sampling distance of `δx` in the first dimension and `δy` in the second dimension.

The plot is shown in the current diagram and a reference to the plot is returned.

The `c` and `m` parameters control the colour scheme. The same algorithm is used for the `MatrixPlot` function; see that article for details.

## Examples

```D ≔ diagram("vector field");
sf ≔ heatmap((x, y) ↦ x^2 + y^2, ❨−10, 10❩, ❨−10, 10❩, '("white", "red"));
vf ≔ VectorField((x, y) ↦ ❨2⋅x, 2⋅y❩, ❨−10, 10❩, ❨−10, 10❩)
```

`heatmap((x, y) ↦ sin(√(x^2 + y^2)), ❨−10, 10❩, ❨−10, 10❩, "red")`

`sf ≔ heatmap((x, y) ↦ sin(√(x^2 + y^2)), ❨−10, 10❩, ❨−10, 10❩, '("blue", "red"))`

`sf ≔ heatmap((x, y) ↦ sin(√(x^2 + y^2)), ❨−10, 10❩, ❨−10, 10❩, '("blue", "white", "red"))`

`sf ≔ heatmap((x, y) ↦ sin(√(x^2 + y^2)), ❨−10, 10❩, ❨−10, 10❩, x ↦ hsv(360⋅x, 1, 1))`