Built-in Mathematica Symbol

DynamicModule

DynamicModule[{x, y, ...}, expr]
represents an object which maintains the same local instance of the symbols x, y, ... in the course of all evaluations of Dynamic objects in expr. Symbols specified in a DynamicModule will by default have their values maintained even across Mathematica sessions.

DynamicModule[{x=x₀, y=y₀, ...}, expr]
specifies initial values for x, y, ....

MORE INFORMATION

DynamicModule first gives unique names to local variables in expr, just like Module, then evaluates the resulting expression, and then returns a version of this wrapped in DynamicModule.

In a notebook, this returned version will often be displayed in an output cell. An example is the output from Manipulate.

If interactive changing or editing of Dynamic objects within the displayed form of a DynamicModule results in changes in any values for local variables, then the DynamicModule object is modified to reflect these.

Values of local variables in a DynamicModule are by default automatically saved when a notebook containing the DynamicModule is saved, so that these values in effect persist across sessions of Mathematica.

If you make a copy of a piece of a notebook that contains a DynamicModule object, the local variables in the copy will be independent of the local variables in the original, though they will start with the same values.

The following options can be given:

Deinitialization	None	an expression to evaluate when the DynamicModule can no longer be displayed
DynamicModuleValues	Automatic	dynamically updated data on variable values
Initialization	None	an expression to evaluate when the DynamicModule is first displayed

When DynamicModule is first evaluated, initial assignments for local variables are made first, and then any setting for the Initialization option is evaluated.

When a DynamicModule object is displayed for the first time in a particular notebook, saved values for local variables are restored, and then any setting for the Initialization option is evaluated.

All values of local variables are saved. Ordinary values of symbols are saved in the first argument of the DynamicModule; other values are saved in the setting for the DynamicModuleValues option.