eli5: How do Perlin noises and graphs come together?

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I am currently researching about terrain generation using Perlin noises. I understand the basic of how they function, but I am still confused how can Perlin noises would be used along with graphs(graph here I mean like how Sine graph used to determine the frequency of mountains).

Perlin noises are used to see different heights of the map, and graphs are also used to see the heights? How do they work together and what are their jobs?

I know this is a more “coding/game dev” question, but I am writing my math essay about because the math behind it seems very interesting.

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Perlin noise is generated by combining multiple layers of noise together, each with a different frequency and amplitude. This allows the resulting noise to have a more organic and natural appearance, rather than a repeating or regular pattern.

When creating terrain using Perlin noise, a graph is used to visualize the resulting noise values and understand how they relate to the terrain. The x and y axes of the graph represent the coordinates of the terrain, and the z axis represents the height of the terrain at that point. The resulting noise values are plotted on the graph, and can be used to determine the height of the terrain at each point.

The relationship between Perlin noise and graphs is that the noise values generated by the Perlin noise function are used to determine the height of the terrain at each point on the graph. This allows the terrain to be generated in a natural and organic way, with smooth transitions and realistic features.