Arc Form Discovery Widget
This Demonstration implements a generate-and-test paradigm for exploring forms constructed by joining semicircles at evenly distributed points along a line. In spite of its simplicity, this "minimum inventory/maximum diversity" system is astoundingly expressive and a rich source of design ideas.
This Demonstration accompanies the wolfram.com blog post, "Minimum Inventory, Maximum Diversity". Because of restrictions on Demonstrations, clicking forms in the sample pane will not pop up a second interface with which to explore the form.
Each click of the "more" button generates a sample of forms with the specified number of connection points and left and right arcs. Use filters to select characteristics of the generated forms, for example, forms with rotational symmetry or forms with an outer circle.
Some combinations of filters and form controls may yield no forms, or very few forms. For example, the Rotational Symmetry filter will yield no forms unless the numbers of left and right arcs is the same. If after clicking "more" the progress bar is advancing too slowly, readjust the arc or filter settings to increase the yield.