# Fields as Functions Mapping Space to Physical Quantities A field in physics is a quantity that's defined at every single point throughout a given space, allowing these quantities to vary from one point to another. This fundamental concept is crucial across various physics branches, from electromagnetism and gravity to fluid dynamics. Whether it's a scalar field assigning a single numerical value (like temperature) or a vector field assigning both a magnitude and direction (like wind velocity) to each point, fields are essentially a map from a "base space" to a space of values. They are vital for describing physical phenomena locally, meaning the value of a field at one point doesn't directly depend on values at other points—a property known as locality, which is a cornerstone of many physical theories. While the mathematics can seem complex, you encounter fields daily, like temperature maps or weather forecasts illustrating wind patterns. > [Cloud computing facilitates diverse field visualizations and analyses, offering animated results for concepts like affine spaces and charge-generated electric fields, interactive web tools for understanding volume elements and 3D scalar/vector fields, and plotting capabilities for showcasing density gradients, surface normals, and various vector field properties.](https://viadean.notion.site/Fields-as-Functions-Mapping-Space-to-Physical-Quantities-2331ae7b9a3280519ea6c7007ca53d40?source=copy_link) ### 🎬Animated result and interactive web {% embed url="" %} Affine space and Coordinate System {% endembed %} {% embed url="" %} 2D-the mass of a sphere with a position-dependant density {% endembed %} {% embed url="" %} a gravitational acceleration vector at each point in space {% endembed %} {% embed url="" %} the mass of a sphere with a given density field {% endembed %} {% embed url="" %} integral force density over a volume {% endembed %} {% embed url="" %} the electric field vectors around a point charge using Gauss’s law {% endembed %}