Spirolaterals as Artwork

A number of different attempts have been made to use the forms generated by the spirolaterals in two-dimensions to create actual artwork.  Having the design generated within a CAD package allows for the simple drawing of it using a variety of line thickness; no different then drafting the same manually.  No attempt has been made to replicate an individual form for the use as a pattern in fabric design or in a similar application.  That possibility could still be investigated.  A second version was tried using a continuous piece on wire, bent according to a diagram of the design.  Somewhat more successful, it gave the design a physical depth but due to overall scale and some of the turning angles, the angles were difficult to reproduce or the smallest length became too small to handle well.  In addition, the spiraling and overlapping nature of the designs caused a layering of the wire that made it difficult to work with on complex forms.  A third version used a continuous strip of putty on glass to replicate the design. This gave results that were somewhat more interesting.  The softer material solved the problem with the turns and overlapping; and the "three-dimensionality" added to the drawing quality of the work.  Work continues using this method.

Since the underlying concept is to have these design be able to be generated by anyone and then produced into some type of physical form, a series of programs have been written to generate spirolaterals.  The first ones written in Microsoft QuickBASIC for computational inquiry and AutoCADís AutoLISP for visualization.  The first version simply used a single line to represent each spirolateral.  Visually it was very weak.  A line thickness was added.  The forms turned from simple line drawings to iconic symbols.  As the line thickness was increased, the open areas between the lines began to close and a totally different form emerged.   Once the basics were understood a JAVA version as written to display the spirolaterals on the web.  Figure 10 displays the JAVA version.  This version can be found at: on the main page of this web site.

Figure 10: JAVA program to generate spirolaterals

The current web version includes two JAVA modules.  The first has a selected group of spirolaterals that generate their reversals as a continuous display.  Each is created line-by-line, erased, and then another is generated.  The second module used the same set of spirolaterals, but enables the viewer to modify the line thickness and browse through each of the reversals, Figure 11a. 
In addition to displaying the line thickness, options are included to add the centerline and edge lines or both for each.  Figure 11b, c, and d display these variations.  These options displayed the internal geometry of the spirolateral that was somewhat lost to the line thickness. 

                                     a. Line thickness                                                                            b. Centerline

                                     c. Edge lines                                                                            d. Center and edge lines

 Figure 11: Variation of thickness and lines



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