A growing picture pattern is usually presented in the form of squares, but it can involve other shapes. Several pictures (usually at least three) are shown demonstrating a growth pattern from one picture to the next. The idea is to spot how the first picture transforms into the second, the second into the third, and so on. The way the transformation takes place is governed by a fixed rule which can be applied indefinitely to create more pictures. The aim is to find the rule and describe it in words or in mathematical terms.
EXAMPLE
First picture shows a single small square.
Second picture shows the single square surrounded by other squares in a 3 by 3 arrangement.
Third picture shows the 3 by 3 arrangement surrounded by other squares to create a 5 by 5 arrangement.
A rule has been established which can be expressed by a mathematical sequence:
1, 9, 25, ... or 12, 32, 52, ...
The rule can be referred to as a rule of evolution, how one shape evolves into the next.
The growing picture pattern is quite similar to successive terms in a mathematical series, but is probably more interesting because it involves pictures, which are more appealing than abstract numbers.