039 The Lofted Architecture of Magic Squares

The Lofted Architecture of Magic Squares

Definition

‘a magic square is an arrangement of distinct numbers (i.e., each number is used once), usually integers, in a square grid, where the numbers in each row, and in each column, and the numbers in the main and secondary diagonals, all add up to the same number.’

Source: https://en.wikipedia.org/wiki/Magic_square

Proposal

Magic Squares are examples of a tool communicating an order, an arrangement. They are both sequenced and chaotic in nature. They indicate an understanding of the principles of mathematical knowledge and the need to communicate that knowledge to allow it to be sensed, analyzed and communicated by other human beings.

This is their apparent complete Architecture.

They also have a 3 dimensional component that can be expressed as part of their Architecture.

Method

The following method is proposed to establish this hidden component of the Architecture in any ‘Magic Square’.

Create a square node grid the size of the ‘Magic Square’.

Add cubes vertically to each of the nodes in the ‘Magic Square’ equal to the amount in each square.

Taking each level of cubes in turn; from the top level to the base level; select each cube edge and connect it using spline curves to form a perimeter.

Remove the cubes leaving the splines in place.

Loft surfaces between each of the spline curves to form unique envelopes at each level

The splines reduce the interpolation error inherent in connecting each perimeter and level by creating smoothing effects between each shape.

They evolve the original primitive shapes into a more efficient form.

Texture the surface of the model.

Results

These forms are considered to be potential process outcomes that are additional components of the Architecture of any ‘Magic Square’.

The results are displayed in the following animation sequences.

The animations are formed by extracting scenes from the models in 360 degree panoramas that can be used in virtual reality systems to utilize each model as an environment.

References

Google Sketchup 8 2010 Original Google Product Free version.

Plugins for Sketchup 8 2010 Original Google Product Free version.as listed with relevant authors from http://www.crai.archi.fr/rld/plugins_list_az.php

Ian K Whittaker

12/04/2016

362 words over 1 page

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