The key difference between a growing pattern and a repeating pattern lies in whether the pattern's elements change according to a rule of increase/decrease or if they simply repeat a core unit.
Here's a breakdown:
Repeating Patterns:
- Definition: A repeating pattern is a sequence where a specific unit or motif repeats consistently.
- Characteristics:
- Contains a unit of repeat which is the smallest set of elements that is copied.
- The elements within the unit of repeat remain constant.
- Predictable and consistent.
- Example: ABABABABAB (The unit of repeat is "AB")
Growing Patterns:
- Definition: A growing pattern is a sequence where the elements change systematically, increasing or decreasing according to a specific rule.
- Characteristics:
- Elements are not simply repeated.
- There's a defined rule for the change in elements.
- May involve numerical sequences or geometric shapes.
- Example: 1, 3, 5, 7, 9 (Each number increases by 2) or a sequence of squares where the side length increases by 1 each time.
Table Summarizing the Differences:
| Feature | Repeating Pattern | Growing Pattern |
|---|---|---|
| Core Principle | Repetition of a unit | Systematic Increase/Decrease |
| Element Change | Elements remain the same | Elements change according to a rule |
| Predictability | Highly predictable | Predictable based on the rule |
| Example | ABCABCABC | 2, 4, 6, 8 |
In summary, while both are types of patterns, repeating patterns involve the consistent repetition of a core unit, whereas growing patterns involve a systematic change (growth or reduction) according to a defined rule.
