Short Answer 
The Geometric Period of ancient Greek art was marked by the emergence of linear motifs, such as spirals and diamonds, particularly in vase painting. Originating in Athens, this period saw a flourishing of creative styles following the Greek Dark Ages, and the geometric designs spread through trade, influencing regional art and laying the groundwork for future artistic developments.
Step 1: Understanding Linear Motifs
During the Geometric Period of ancient Greek art, linear motifs became prevalent. These motifs included various geometric patterns such as spirals, diamonds, and cross hatching. This stylistic method significantly influenced the appearance of many artistic works from this era, primarily seen in vase painting.
Step 2: The Geometric Period Overview
The Geometric Period of Greek art occurred after the Greek Dark Ages and is a time when Greek art flourished remarkably. It is characterized by a resurgence of creativity and culture, leading to the development of distinct artistic styles. This period is most notable for its geometric designs and shapes that adorned everyday objects, especially pottery.
Step 3: Cultural Spread and Influence
Initially centered in Athens, the Geometric style began to spread to other Aegean trading cities through trade and cultural exchange. The popularity of these geometric motifs allowed them to influence regional art and established a foundation for future artistic developments in ancient Greece.