CHRISTOPHER MADDEN

contemporary art - the generation of form from underlying symmetrical shapes

Complexity from Simplicity

Introduction

This page is an explanation of the concepts and techniques behind my series of artworks titled Complexity, started in 2007.

These works, which are predominantly and deliberately in black and white, were a precursor to my later animations in that the techniques developed for them were used in the later works.

Above: the first, and simplest, work in the series, titled In the Beginning.
The explanation is divided into three sections.

The underlying structure of the work

The underlying concepts behind the work

The underlying structure of the universe

The Underlying Structure of the Work

Emergent Patterns

optical art - op art - the shifting perception of pattern

The artworks on this page comprise an investigation into the concept of the generation of complexity from simplicity.

The simplest works in the series consist of videos and static images of two uniform grids of black lines or dots that are positioned one directly above the other and then rotated relative to each other. In the areas where the black on the top grid directly overlays the black on the lower grid the blacks cancel out, leaving white.
optical art - op art - the shifting perception of pattern

Other works in the series build on this basic concept by introducing more variation, such as by adding colour or by distorting the grids. The example below, for instance, consists of two grids of regular lines in which one of the grids is made to bulge very slightly. For the purposes of this explanation however, I'll stick with the simple black and white regular grids, as the other variables tend to obscure the underlying principals by making the generative processes involved more opaque.

optical art - op art - the shifting perception of pattern

The patterns produced by the overlapping grids in the works have some superficial similarities to Moiré patterns, in which two overlapping patterns generate secondary optical effects. Unlike Moiré patterns however, the elements in the Complexity series actually interact with each other rather than simply overlap, resulting in the potential for infinitely more complex patterns (Moiré patterns are self-limiting due to the nature of their production).

science and art - the generation of complex patterns from simple patterns
As you can see in the examples here, the emergent patterns in the works seem to contain multiple discrete overlapping 'entities' that each possess their own individual radial symmetry - in fact, no part of the internal structure of the interacting grids is not part of several such entities at once. The entities often seem to 'bubble' in and out of existence as the eye scans the images in the static versions or as the layers move relative to each other in the videos. An important property of these entities is that they are not present in the original structure but that they have been created as a by-product of the process behind the work.

The complexity exhibited by the entities seems highly disproportionate compared to the simplicity of the uniform grids that generated them.

More than two grids can be overlaid at the same time. The image below shows the pattern generated by four overlaid grids – notice how much more complicated this is than the previous pattern generated by two grids.

op art - layers of complexity in patterns
The complexity of the patterns can become quite extreme if there are multiple grids overlaying each other, to the point where the resulting complexity in the patterns can be so extreme that the human brain is incapable of discerning all of the levels of complexity. The image below shows a small detail of a multi-grid work, indicating the almost indecipherably complicated degree of internal complexity that can be generated with multiple grids.

contemporary optical art - complex pattern generation
The videos are particularly effective at drawing the viewer's attention to the process by which the patterns created by the overlapping grids are generated. This is especially the case in examples where one of the grids in the video is static, emphasising the fact that the complex patterns observed are the result of nothing more than one grid rotating above another.

The Underlying Concepts Behind the Work

Creation (plus Religion)

Creation

The initial inspiration for this series of images and animations stemmed from my interest in science and philosophy, and specifically in my interest in questions concerning the underlying nature of physical reality and our perception of it.

The original motivation behind the work was a wish to devise a visual means of expressing the concept that our complex universe is generated from the interaction between extremely simple fundamental forces that underlie the cosmos. There's more on these fundamental forces later.

optical art - op art - the shifting perception of pattern

While the dynamic expressed in the works in the series was primarily concerned with the creation of complex forms at the most fundamental phenomenal level of the physical universe, the work can also be interpreted as a representation of the manner in which the complexity within the universe cascades outwards creating higher levels of reality.

Thus the universe becomes inevitably more complicated and phenomena-rich. For example, the fundamental forces underlying the universe lead to the creation of quarks, leading to the creation of atoms, leading to the creation of molecules, leading to the creation of stars, leading to the creation of planets leading to the creation of life, leading to the creation of consciousness.

Essentially, the work is an attempt to visualise the concept that all phenomena in the universe emanate from the first simple forms that underlie the physical structure of the entire cosmos.

Religion

The fact that the images in the series generate patterns that we find immediately arresting is also a significant aspect of the work. Humans are pattern-seeking creatures, constantly attempting to find structure and form in things (even where it doesn't exist, such as in Rorschach tests or cumulus clouds). Notice the way that the eye darts from pattern to pattern within some of the static images such as the one below as the brain tries to pin down the form within the piece.

contemporary art - the generation of form from underlying symmetrical shapes
Several of the works, especially in their static form, bear a resemblance to religious symbols such as crosses, stars and roundels, or even to religious architectural structures such as stained glass rose windows. This resemblance is unintended but fortuitous, in that it meshes with the fact that the works are at their core intended as symbols of the generation of structure (and meaning) within the universe, which is also a core concern of religion.

religious art, creation and science islamic roundel - the circle in art
Christian and Islamic imagery

Another allusion to religion can be found in the way in which the symmetry of many of the patterns that are generated within the works suggests the idea of order within complexity, mirroring the manner in which religion seeks to find order in a seemingly chaotic universe. Here again the parallel with religion was unintended but is valid.

The Underlying Structure of the Universe

A Universe that Hangs on Either Side of Nothingness


science and art - the generation of complex patterns from simple patterns

Elsewhere on this page I've described briefly something about the visual dynamics that generate the patterns in the artwork and the symbolism and meaning within the work.

This section explains the thinking that prompted my work on the first pieces in the series – those composed of uniform grids of black dots – with specific reference to the metaphorical allusions that were applied to the work.


The Genesis of In the Beginning

The primary purpose of In the Beginning was to express visually something about what I imagine as the underlying structure of reality.

Briefly, the work uses a metaphor in which a square grid of uniform black dots represents the deepest, most fundamental and basic level of the physical universe, where nothing exists other than the simplest possible fluctuations in 'nothingness' itself (represented by the uniform dots).

Complexity and structure comes into existence when the grid of dots interacts with itself, creating intricate forms that contain their own internal structure.


The explanation in more depth

At the lowest level of physical reality – below the atoms that form the elements of our universe, below the electrons, protons and other subatomic particles that form those atoms, below the quarks that form those subatomic particles – lies a state of 'nothingness', a level at which nothing exists.

This level of nothingness is impossible to visualise, so we have to resort to woefully inadequate metaphor. One way to imagine the state of nothingness is to see it as being like the absolutely flat surface of an infinitely vast ocean in which there is nothing above the surface and nothing below the surface: the only thing that exists is the surface itself, the interface between above and below. Another way to imagine it is as an infinitely large sheet of some form of insubstantial material that has no thickness at all - something that is there but that doesn't exist.

Now imagine that on the surface of this ocean of nothingness or sheet of nothingness a 'disturbance' occurs.

Employing metaphor, the disturbance can be visualised as a 'ripple' meandering across the surface of the endless flat ocean of nothingness or across the infinite sheet of nothingness.

The words 'disturbance' and 'ripple' are in inverted commas because at the level of nothingness involved there can be nothing to create a disturbance as we understand it. Time, space matter and energy do not exist at this level.

Below is a visualisation of the disturbance as a ripple on a straight line, where the straight line represents the flat surface of nothingness.

It is important that there is only one such ripple or disturbance that has occurred in the vastness of nothingness, as, being at a level of nothingness it is hard enough to summon up a single disturbance, let alone several.

As I will explain, in this metaphor it is this single ripple that gives rise to all of the phenomena within the universe.

Like waves in general, the ripple in the image above rises above and drops below the flat surface that is a metaphor for nothingness. The consequence of this is that in terms of energy (or rather, what is analogous to energy at this rarified level) the ripple adds nothing and takes away nothing from the level of nothingness, as the 'energy' in the peak and the trough cancel out (as shown in the 'energy' graph of the ripple below). So, even though there is a ripple, the sum total of its existence neither adds to nor subtracts from the all pervading nothingness.

Because the ripple that creates the universe straddles the line of nothingness rather than 'rising up from it', it can be conceived that 'the universe hangs on either side of nothingness'.

How does a single ripple manage to generate a whole universe?

In the image below, a portion of the ripple is seen from above, represented by a gray line on the empty whiteness of the page.

The metaphorical ripple is perhaps endlessly long (because at the level of nothingness there is no end to the nothingness), and there is nothing to stop the ripple meandering freely across the entire surface of nothingness.

In its meanderings the ripple will inevitably cross itself, as shown in the image below. Where it does so it interacts with itself, creating a secondary disturbance - analogous to the way that ripples or waves in water interact when they cross each other. This secondary disturbance is represented in the image by a black dot.

As the single ripple twists and turns it intersects itself multiple times, creating a proliferation of these secondary disturbances. Thus it is that multiple phenomena, in the form of the secondary disturbances, can be generated by a single initial phenomenon (in the form of the ripple).

It is these secondary disturbances that I want to concentrate on now, so in the image below the dots that represent the secondary disturbances have been isolated from the ripple that created them.

When two secondary disturbances, represented by the dots, are generated in such close proximity that their areas overlap, the disturbances interact in the overlapping area, creating a third level of disturbance - indicated by the colour in the image below.

There's a special case example of this third level of disturbance, in which the third disturbance is actually a cancelling out of the second disturbance, indicated in the image below by the way that the overlapping area has reverted to nothingness in the form of white space.

This manifestation of complexity, in which the disturbances cancel out, is in some ways more interesting than the manifestation in which a new level of complexity - a new colour - is created, because it creates a greater degree of complexity (in the form of a complex shape) without the addition of a new quality of complexity (the colour).

It is this manifestation of the increase in complexity that is explored in the artworks on this page.

In the Beginning takes as its foundation a simple regular grid of dots as a visual representation of the disturbances that are generated only a few degrees of complexity above the underlying nothingness that lies at the foundation of physical reality. This grid could be interpreted as a visual metaphor for the base layer of 'the fabric of the universe'.

The dots are not randomly positioned as in the earlier image but are arranged in a regular grid. This is primarily for metaphorical purposes, as a representation of simplicity, however the layout could equally represent an inherent ordering of the dots due to a natural process that is analogous to (but not the same as) the way that a single layer of spheres such as balls would naturally form a regular array when fitted tightly into a confined space (which may apply if an infinite number of disturbances had to fit into the expanse of nothingness, even though the expanse of nothingness is infinite itself).

In the array shown above there are no interacting dots to form secondary disturbances, so the effect is a uniform, continuous conformity or continuum of black dots.

In order to create interacting dots (as shown in the images below) a second array of dots, identical to the first, is inserted directly into the same space as the first array and is then offset so that the two arrays are not coincident with each other. (These two arrays of dots should ideally be thought of as occupying the same space or level as each other, although when observing the artwork it's very hard not to interpret them as being separate arrays one above the other.)

art and science - the perception of pattern
science and contemporary art - the perception of pattern

The interaction between the arrays of dots instantly generates a number of highly complex and intricate patterns, with all of the areas where the black dots of the two arrays coincide cancelling out to leave white.

As mentioned earlier, the emergent patterns seem to contain multiple discrete overlapping 'entities' that seem to 'bubble' in and out of existence as the layers move relative to each other in the videos or as the eye scans the images in the static versions.

It is this manifestation of great complexity resulting from the interaction of simple forms that I see as a metaphor for the process that underlies and generates the structure of the universe.