01
Define what is allowed to change
A dynamic model needs a state: the information carried from one step to the next. That state might be a single number, a position or a collection of interacting values. A project using this name could begin every example by naming that state in plain language. The recurrence here tracks only x, so there is no hidden velocity, resource pool or external input. Making the state explicit helps readers resist importing assumptions from the visual appearance of a diagram into a mathematical rule that does not contain them.
02
An open theme still needs boundaries
Unbound can suggest creative range without meaning that every model lacks limits. The capped version of the exercise demonstrates the distinction. Its state cannot exceed 10 because that condition is part of the update rule. A project can explore both constrained and unconstrained behaviours under the same identity. The useful editorial choice is to show the boundary rather than conceal it. A reader then understands whether a flat segment comes from the rule, from a display limit or from a missing observation in an actual data series.
03
Make step numbers part of the explanation
Step zero is the initial state, and step one is the result after one application of the rule. Confusing those labels shifts every comparison. UnboundDynamics could adopt a consistent table format that includes both the step number and the state value. An animation can use the same labels so the visual and written descriptions agree. This is especially useful when a short sequence is discussed in prose, because phrases such as after four steps then refer to a precise row instead of an ambiguous count of displayed values.