Different arrangements of the same number of elements will have different configurational properties.
Here are a set of arrangements of the same eight square cell.
Shapes as configuration in effect we are treating a shape as a graph, which is a relation complex that temporarly ignors other attributes of the elements and their relation.
A configurational discription is not to understand it's shape and its properties, but to give insight into properties of spatial and formal shapes which manifest themselves as the most fundamental. This property of spatial shape are significantly different when seen from different points of views within the graph. This can be demonstrated using the j'graphs on the earlier shape configurations.
By drawing j-graphs of all nodes in a shape, then, we can picture some deep properties of a shape. A highly interesting property of shapes is the number of different j-graphs they have, and how strong the differences are.
For example, showing all the possible j-graphs in these two selected shape configurations. The number varies from 3 to 6. The reason for less numbers of j-graphs in the first diagram is that if the two nodes have identical depth numbers, this means that from these two points of views, the shape has a structural identity, which can be identified as symmetry. Therefore, the less number of different j-graphs means more of the shapes appear regular beacause there ae more symmetries in the shape.
The aspect of the structure of these graphs thus seems to reflect our sense that shapes can be regular or irregular to different degrees.
The j-graph allows us to look at symmetry as an internal property.
Here are a set of arrangements of the same eight square cell.
A configurational discription is not to understand it's shape and its properties, but to give insight into properties of spatial and formal shapes which manifest themselves as the most fundamental. This property of spatial shape are significantly different when seen from different points of views within the graph. This can be demonstrated using the j'graphs on the earlier shape configurations.
For example, showing all the possible j-graphs in these two selected shape configurations. The number varies from 3 to 6. The reason for less numbers of j-graphs in the first diagram is that if the two nodes have identical depth numbers, this means that from these two points of views, the shape has a structural identity, which can be identified as symmetry. Therefore, the less number of different j-graphs means more of the shapes appear regular beacause there ae more symmetries in the shape.
The aspect of the structure of these graphs thus seems to reflect our sense that shapes can be regular or irregular to different degrees.
The j-graph allows us to look at symmetry as an internal property.
No comments:
Post a Comment