Moiré Patterns

Dutch Invertuals – ‘Cohesion’

Moiré 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 moiré effect is created in the eye of the viewer, disparate from the shapes formed by the individual patterns themselves.


A moiré pattern generated by overlapping two identical patterns of concentric circles

Associated mathematical formulas can be used to determine the size and spacing of inferred moiré patterns from a series of regularly spaced overlaid patterns. The beauty of the moiré 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.

Physical Moiré experiments

The video above illustrates the moiré 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 moiré 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 physical experiment above illustrate the potential of moiré 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 moiré 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:

Moire Overlay   The linear moiré overlay       Resultant Shape

The moiré underlay  creating the circular motion 

This moiré 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 moiré animation.

Brief 01_Moire System Analysis_Linear Animation-page-001

Rules for defining a moiré ‘underlay’ for linear animation

Whilst primarily a visual effect it is the ability to translate spatially which gives the moiré 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 moiré patterns……

Moiré – Julias Horsthuis

Updated Research:

Video illustrating various physical moiré experiments


Rules for defining moiré patterns in linear gratings


Mathematical rules for defining moiré patterns of rotation


Physical model for experimenting with moiré rotation patterns



Results from the physical model using sin curves & square gratings

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


Digital tests and physical proofs of programming moiré

Moiré patterns work in both ‘positive’ and ‘negative’ constructions. Positive moiré can be classed as additive, constructing patterns consisting of lines to create the effect. Negative moiré 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 moiré patterns.


Negative moiré, 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 moiré effect, sin curve gratings were mapped onto the faces of a cube, at varied rotations. The effect is a spatial understanding of moiré patterns when the various faces of the cube overlap. The moiré 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 moiré patterns in three dimensions

Mirror Muses

Mirror Muses_01Mirror Muses_02 Mirror Muses is an installation inspired by research into anamorphosis derived from the Greek prefix ana‑, meaning back or again, and the word morphe, meaning shape or form. Specifically this is the investigation of distorted geometry which can be reconstituted into its true from when viewed in the reflection of a mirrored object. The proposed installation for this years burning man festival is an anamorphic projection of two Greek muses; Melpomene & Thalia, the muses of comedy and tragedy. Each of these projections faces a convex half-cylindrical mirror, in which the sectioned and distorted faces are reconstituted from an unrecognisable geometry back into their recognisable forms. Night 01 - BackNight 02 - Detail At night the proposed installation will be lit with EL wire. This will provide a light source, illuminating its presence to burners from a distance whilst also ensuring that the anamorphosis can take place throughout the night, allowing the reflections of both muses to brightly contrast the reflection of the night environment. 02 - Back Sun_Photoshop The installation is approximately 2.4m tall (defined by each of the mirrors) with each projection at around half that height. This enables the hollow timber sections to be laser cut from standard plywood sheets. Mirror Muses_Burning Man_P9 A structural platform would be constructed from 2″x 2″ dimensional lumber with 3/4″ gaps to allow the plywood timber sections to slot in between. These would be bolted together using cross dowels to lock each piece into place, the stairs and viewing platforms are constructed in a similar manner to create one structural component. Mirror Muses_Burning Man_P10Mirror Muses_Burning Man_P1103c - Reflection Detail Close

System Development: The Inversion Principle


The Inversion Principle is a mathematical formula that maps points from inside to outside a circle and vice versa, governed by the equation MQ = r2/MP where [MP] is the distance between the origin of the circle and a chosen point and [r] is the radius of the circle. The chosen point is then moved along motion vector [MP] at new distance [MQ].


Initial experiments explored inverting a series of two dimensional shapes through a circle. Each shape or series of curves was first divided into a series of points which were remapped using the inversion principle and then reconnected with the same relationship.


The same process can be applied to three dimensional objects, using a sphere as the inverting object as opposed to a circle. Below is the inversion of an Icosahedron, achieved by dividing the initial shape into a series of vertices defining the faces. These are remapped by the Inversion Principle and then reconnected with the same relationship to give new vertices and faces.


Exploration into the number of subdivisions showed that the more vertices a shape is divided into, the more it approaches its ‘true’ approximation. Less subdivisions leads to a more faceted output geometry.


These experiments were followed by a series of physical models which investigated modelling the interior volumes of the 3D object as a series of two dimensional planes using both spheres and cylinders as the inversion object. Below are the internal volumes of an inverted Dipyramid and four sided pyramid.