## 19th October 2015 Tutorials

Hello Everyone – Back in our studio studying mathematical, biological and made-made systems using parametric tools and digital fabrication for our BRIEF01: EXPLORE. Here are couple highlights from yesterday’s tutorial showing the initial study models and drawings needed to explain the rules of the system and their creative possibilities.

Dutch Invertuals – ‘Cohesion’

MoirÃ© patterns are superimposed secondary patterns created when two static surface patterns are overlaid one on top of the other. By displacing or rotating one or both patterns a new visual pattern becomes visible separate to the geometry of the first two. This moirÃ© effectÂ is created in the eye of the viewer, disparate from the shapes formed by the individual patterns themselves.

A moirÃ© pattern generated by overlapping two identical patterns of concentric circles

Associated mathematical formulas can be used to determine the size and spacing of inferred moirÃ© patterns from a series of regularly spaced overlaid patterns. The beauty of the moirÃ© effect is the illusion of movement created through completely static overlays. This forms a naturally interactive experience for the participant, giving over control to the superimposed pattern through visual movement and rotation.

The video above illustrates the moirÃ© effect in two dimensions by overlaying static linear and concentric patterns, printed on acetate, and manipulating their motion and rotation in order to create a new visual pattern.

Concentric and Linear patterns, printed on acetate overlays

This effect is not restricted to two dimensional patterns but can also be applied in three dimensions. These spatial patterns then utilise the motion of the viewer in order to manipulate the moirÃ© effect. The video below illustrates how three dimensional sculpted elements, set on separate spatial planes can form a visual pattern and take advantage of simple motions by the viewer.

Scale model of the facade for Brisbane Girls School Creative Learning Centre – M3 Architects

The two primary resultant effects from the physicalÂ experiment above illustrate the potential of moirÃ© to create alternate visual patterns and to generate the illusion of movement. These were then applied digitally to create an animation that controls these aspects to create a recognisable representation of motion to the viewer, as opposed to an abstract pattern.

Digital testing of the moirÃ© effect in animation

The above digital animation illustrates the rotational movement of a circle through the movement of a linear overlay, created with the two static images below:

The moirÃ© underlay Â creating the circular motionÂ

This moirÃ© underlay is created through a series of rules defined by the size of the overlay and the direction, factor and type of movement (linear or rotational). The diagram below explores the rules associated with this specific type of moirÃ© animation.

Rules for defining a moirÃ© ‘underlay’ for linear animation

Whilst primarily a visual effect it is the ability to translate spatially which gives the moirÃ© effect the potential to be applied in a design context, particularly given it’s interactive nature and the reliance on the involvement of participants in order to reveal it’s true beauty.

The video below takes this concept to the extreme, exploring the effects of imagining matter as nothing more than multi-dimensional moirÃ© patterns……

Updated Research:

VideoÂ illustratingÂ various physical moirÃ© experiments

Rules for defining moirÃ© patterns in linear gratings

Mathematical rules for defining moirÃ© patterns of rotation

Physical model for experimenting with moirÃ© rotation patterns

Results from the physical model using sin curves & square gratings

MoirÃ© patterns can be ‘programmed’ using a certain mathematical formula. If two variables are known; the base layer and the desired moirÃ© pattern (in this instance a sin curve) the resultant reveal layer can be determined, allowing moirÃ© patterns to be programmed to any shape.

Digital tests and physical proofs of programming moirÃ©

MoirÃ© patterns work in both ‘positive’ and ‘negative’ constructions. Positive moirÃ© can be classed as additive, constructing patterns consisting of lines to create the effect. Negative moirÃ© conversely removes elements of material (in this instance circles from card) to create patterns when held at a distance. The bottom row of images shows the most successful variables for discerning negative moirÃ© patterns.

Negative moirÃ©, set-up & physical experiment

The above experiment was digitally reproduced, modelling its negative space in order to understand how the variables of distance affect the reception of pattern.

Digital experiments with distance variables

In order to move from the plane into a spatial exploration of the moirÃ© effect, sin curve gratings were mapped onto the faces of a cube, at varied rotations. The effect is a spatial understanding of moirÃ© patterns when the various faces of the cube overlap. The moirÃ© effect can be created by two distinct methods; a movement by the user, distorting the areas of overlap and the movement of the cube itself, visually shifting patterns.

Physical model exploring moirÃ© patterns in three dimensions