STEM CAD

[Structural Geometric Topology Home] > [STEAM CAD]

Description

STEM CAD is the the creative engine of my mathematical art. It is inspired by the tables Leonardo da Vinci (Da Vinci tables) used to combine exaggerated physical features to generate ideas for his famous caricatures (Figure 1). The system features 5 levels modeled on academia. At each level, there are one or more tables that function as the genrative engines and taxonomic organization of the system. The sections below detail different aspects of its functionality, architecture and operation. 

Step 3. Conceptual Aided Design

Three Kinds of Creativity

These tables have been repurposed as an analogue knowledge engineering system that has been created to optimize artistic productivity by combining three kinds of creativity in one system: structural, tabular, and nested creativity. 

The first is like Lego. But in place of bricks as building blocks, points, lines, polygons, and polyhedra are used as the components with which to build topological structures. 

The second (Da Vinci tables) works like a multiplication table. But instead of numbers, words for components are placed in the left column, words for structures in the top row and the operators construct or deconstruct where the multiplication operator would. Then, the table is filled out with combinations of components and structures that generate ideas for graphic designs. 

The third is like the Russian nesting dolls. In place of the dolls, there are tables inside the output cells of each Da Vinci table in a nested hierarchy. Since STEM CAD has a five-level hierarchy, it means there are five sets of tables one set at each level. The number of table(s) at any given level is determined by the number of output cells of the table(s) at the level above it/them. 

Function

STEM CAD is designed to engineer and reverse engineer STEM knowledge including mathematics that simultaneously generates and classifies it. Composite data structures produced with STEM CAD can be used as the inspiration for graphic designs using a CAD program like Great Stella 4D Pro that are then exported to 3D printer software for physical realization using 3D Printing technology. 

When the system is used from the top down as seen in step 2 of this sites methodology (structural geometric topology) it is generative. When operated from the bottom up it functions like the Linaean taxonomic system; nesting structures in its tabular hierarchy.

Architecture

STEM CAD is organized in a five-level nested hierarchy modeled on academia. The five levels as:

Level 5. University

Level 4. Departments

Level 3. Disciplines

Level 2. Categories of Objects

Level 1. Objects

The STEM University is composed of the Science, Technology, Engineering, and Mathematics departments that when combined produce composite departments (Figure 2). 

(Figure 1)

At the next level down, there are the disciplines that compose each department. The mathematics department in STEAM CAD, for example, would have a predefined set of disciplines with the ability to manual add more. 

Below that are the categories that define each discipline based on the objects each study. For example, the categories of geometry include, points, lines, polygons, and polyhedra among others. 

Operation

A demonstration of how STEAM CAD works in the production of mathematical ideas can be found in Step 2 of the three-step methodology that transforms mathematical ideas into graphical and tangible objects. 

Conclusion

The nesting of tables in STEAM CAD amplify creative productivity exponetially. From two initial inputs at the Departments level and assuming no more that 4 inputs define the input rows and columns of each successive table, the terminal output from the intial input is 256. With the expansion of inputs within levels and or the addition of sub-levels within the hierarchy, the increase in productive capabilities quickly outpaces manual computation. Therefore, dedicated software as yet to be created would be required to manage larger data sets than those depicted here.  However, even at low levels of production, the system is designed to enhance and augment human creativity in the design of structured data sets that can be used as prompts for graphic design and artistic expression. 

Beyond art though, it is possible that STEAM CAD may prove useful in academic design, knowledge engineering, and cognitive mathematics.