SEEING THE THIRD AND FOURTH DIMENSIONS:NEW WORK ON RADIAL SPREADS
Pery BurgeSummary of paper
I continue investigating radial spreads of ink in water. These spreads can be seen in both artistic and scientific terms. New photographic equipment has enabled me to examine these forms more closely, and the use of different inks within one spread enables me to see its different aspects more clearly. Descriptions of how various inks behave when used together, the types of polyhedral shapes that may result, inner structures, and the effects of relatively high speeds on ink flow, are followed by a section on various ink textures - this section is both scientific and artistic. Finally I look at artistic aspects of radial spreads: creating “time-rich” images, and making visual connections between the spreads and organic life-forms and cosmic phenomena respectively.Method of creating radial spreads of ink in water
The method is described in detail in my paper ‘Hidden Patterns: creating radial spreads of ink in water’ Journal of Visualization , Vol.10 No.2: April 2007 pp.171-178.
Combining different inks
Different kinds of inks, when superimposed on the gold paint mentioned in the method, may reveal different aspects of the spread. Some inks mix easily with the water, moving downward and visualizing the spread’s activity below the surface. This can be seen in In Fig.1, where brown writing ink, having mixed well with the water, forms a toroidal vortex emanating from the stagnation point. The yellow fabric ink also used resists mixing, and becomes filamentous beneath the surface and ridged on the surface.
Fig.1 The spread and detail showing the vortex.
The following sequence (Fig.2) shows a similar tendency for two kinds of ink to behave differently, and to occupy different areas of the spread. Blue writing ink and yellow fabric ink were used. In the first frame a blob of ink is waiting to burst above an older spread. When it bursts, most of the yellow ink moves outward, leaving a gap between it and the mainly blue mushroom-shaped vortex. The outward force of the spread causes it to rise out of the water at the back (outlined in gold). The spread’s shape is modified as It continues to move upward in the next frame (more about this phenomenon in the later section about jumping spreads).
Fig.2 Ink behaviours contrasted within one spread
Different coloured inks can accentuate the 3-dimensional nature of the forms created within the radial spread, particularly if light and dark colours are used together.
Fig.3 Blue ink has been placed on top of yellow. Two blobs wait to burst, upper right. Left side of image: two inks mix to some extent in the spread; below right, they remain discrete.
In the new spread in Fig.3, lower right, the yellow networking is linked by a strand of ink to the toroidal vortex forming further down. The blue ink forms its own pattern below the surface. In the older spread, left side of image, form is accentuated by contrasting colours.
Lighter foreground colours register well on a dark background. The following examples (Fig.4) illustrate how foreground patterns can be accentuated by darker background colour.
Fig.4 Two strongly defined spread patterns. Left, the central spread is displacing an older one, causing it to form waves at its edge as it moves out fast. Right, complex networking develops.
Two and three dimensional shapes taking form
In Fig.4 both radial spreads contain many interesting shapes in their networking. In both cases, the yellow fabric ink tends to become filamentous, and is particularly useful for visualizing shapes as in Fig.5.
Fig.5 Patterns taking form. Ink in the central area is still 'filmy' and less well defined than in the strands at upper left, where a definite pattern has emerged.
In such networks familiar shapes may emerge in two dimensions (across the water) or three dimensions (down through the water as well). Oval or circular holes can occur; in groups, these often tend to straighten off at the sides, as they have in Fig.4, both images. The shapes in Fig.4, left image, have features in common with hexagons. I have observed many times shapes in networks which are reminiscent of hexagons. There may be a link with honeycomb patterning where roughly spherical objects may be packed together efficiently (I. Stewart,
What shape is a snowflake? Weidenfeld & Nicolson 2001 p.19). Angled shapes reminiscent of hexagons may also be generated from a central point which will form the common vertex for them as in Fig.6, left.
Fig.6 Left: Spider-like forms in foreground seem to be points of origination for hexagon-like shapes. Middle: Left diagram: progression towards hexagonal shapes. Right diagram: drawing of shapes from foreground of right hand photo. Right: fully formed many-sided shapes interspersed with triangular and square shapes as found in semi-regular tessellations.
The networks often contain other shapes which act as fillers around the hexagons. These shapes are often reminiscent of squares and equilateral triangles. There may be a link with tessellation patterns; it is well known that hexagons, squares and equilateral triangles together form the tessellations found in tiling patterns and polyhedra (I.Stewart, op.cit. pp.74-75); Gasson, P., Geometry of Spatial Forms, Ellis Horwood 1983 pp.225-226). In Fig.6, the right-hand image contains curvy analogs to such tessellations.
The process of shape formation often happens at very early stages of the spread. Fig.7 shows a new spread still moving out very fast, as can be seen by the ink at its edges. Already there are patterns forming in its lower half (detail, middle). Right: a different spread showing three, four and six sided shapes.
Fig.7 Left, middle: a new spread showing somewhat irregular tessellations. Right: many shapes juxtaposed.
Some shapes may look predominantly oval as in Fig.8,left, or mainly undefinable, right. There are also a couple of hexagonal shapes in these pictures. If one looks closely at the left image, a hexagonal-shaped hole is just visible at the centre of the film of ink, and, right, another hexagonal-shaped hole emerges, surrounded by bending filaments of ink.
Fig.8 Hexagons apparent near the stagnation points of each spread.
Elongation of shapes because of the spread’s outward movement can be evident at the edges of the spread (Fig.9). Distortion of shape gives an indication of relative speeds of flow (faster at the edges). The networking is at its most regular near the stagnation point, where hexagonal shapes predominate (Fig.9, main picture, lower area).
Fig.9 whole spread and two details. The most regular patterning is to be found where flow is slower, away from the edges of the spread.
Outlying structures
Regular structures situated at some distance away from the spreads have been observed. It is possible that the outward force of the spread may affect all of the water in the bowl (about 10 cm in diameter), setting up outlying patterns which are visualized by strands of ink. The example in Fig.10, next to the central mass of yellow ink, seems to be a regular shape of some kind.
Fig.10 A large regular shape found outside the radial spread - if it were complete, I believe it would have 14 sides.
A macro lens has revealed a good deal of information about the structures of radial spreads well below the surface of the water. Sometimes these structures form as a result of ink falling downward during the initial action of the spread (as in Fig.3 above, where the ink linking the upper networking with the toroidal vortex is clearly visible). The falling ink moves at a relatively slow speed, and vortices therefore have time to form. Toroidal and leapfrogging vortices are both common features of these structures (Fig.11).
Fig.11 Left: Below the spread's somewhat blurred networking, and underneath its stagnation point, a structure takes form with toroidal vortices, centre, encircled by leapfrogging vortices. Right: the lower structure is joined to the edge of the spread, lower right, and has ink folding through itself to form a complex structure below the networking.
A symmetrical cluster of vortices formed from thin ribbons of ink appears in Fig.12, centre.
Fig.12 The central structure seen through the gap in the networking has interesting geometric features, including the zigzag formation at its base.
Visualizing the speed of flow of radial spreads
It has been mentioned above that there appear to be different rates of flow within the confines of the radial spread. Regular patterning may be subject to modification and shapes may elongate (Fig.9). Taken as a whole, the spread may move at varying speeds. For example, the amount of ink in the surrounding water will affect flow rate; the more ink there is, the slower the spread will progress. The less ink there is, the faster and larger the spread.
High speeds manifest themselves in various ways. Sometimes a spread may reach the side of the bowl and rebound, causing a backwash as in Fig.13.
Fig.13 Rolling water on its way back from the side of the bowl (top, just seen).
Upward jets in fast-moving spreads can be several centimetres long (Fig.14). As an indication of size, the central blob of ink is about 1cm wide.
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Fig.14 Upward jets, marked on the right by a chain of vortices.
The sequence below in Fig.15 shows how the quality of line that the ink takes demonstrates the relative rates of ink speed flow. The upper layer of ink forms scalloped lines; underneath, yellow ink joined at the stagnation point develops its vortices.
Fig.15 These three pictures are separated in time by two and three seconds respectively.Jumping spreads
Photography (as opposed to the naked eye) shows that some spreads are moving so fast that they lift right out of the water. The sequence in Fig.2 shown earlier on p.2 again shows the circular form of the spread changing, as its back end lifts into the air, taking the gold paint with it. Its quasi-dumb-bell shape becomes more pronounced as the spread lifts itself up higher (3rd frame). The time intervals between the pictures are 12 sec., 2 sec., 4 sec. respectively.
In Fig.16 below the spread’s circular shape is changing into an oval because it is no longer supported by the water
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Fig.16 There are four and three second intervals respectively between these pictures. The long shapes made by the ink inside the spread are another indication of how it is stretching upwards.Artistic aspects
A new awareness of the different qualities of ink has prompted me to think of these images in terms of texture. The ink may look solid, as if it were rope or string; it may appear to be elastic like bread dough, or it may look like a piece of paper torn in half. Scientifically speaking, the characteristics of ink can be viewed in terms of its chemical composition or perhaps its Schmidt number. Artistically speaking, the inks take on an aesthetic value partly because they are beautiful in themselves, but also because they remind us of other things (Fig.17). There is a certain magic about liquid looking like rope or paper, for instance. Bearing this in mind, it seemed appropriate to form a collection of images representing various textures. Placed side by side, the contrasting forms that the ink takes are shown to their best advantage. Scientifically speaking, a collection of images of this sort, combined with a knowledge of the chemistry of the inks, would form a useful profile of the materials.
brittle mesh; painted metal; brown sugar; torn tissue
Above: plant stem; lightning trails; lace; gauze; below: string; dried acrylic paint; jellied sweets; decorative glass
Fig. 17 Parallels between ink and other materials
Organic Forms
Radial spreads are reminiscent of organic forms in their ‘birth, life and death’. New examples of this idea are to be found, for instance in ‘Monochromaforms’ (Fig.-19), left, where three main stages of the spread form are to be seen in three separate spreads. ‘Microform’, has an inner structure, discussed earlier, which emphasizes its organic quality.
Fig.18 Life-like forms. Left, three stages of the spread; one about to burst (top left), and at centre a new spread and a dying spread face to face. Right, a jellyfish-like form.
An increased consciousness of visual links between the small-scale world of ink in water, and large-scale objects such as new stars, has led me to explore images that are deliberately ambiguous. Many of the images invite different interpretations. The two chosen below in Fig.-20 to illustrate this point also have a time-rich aspect. ‘Sugar-flow’, left has granulated gold flowing out of the channel created by the colored inks. It could be seen as sand and water close up or an aerial view of land and sea masses. ‘Colored time’, right, has gold blurring where the paint is moving really fast, as opposed to the ink underneath, whose patterns are more well-defined. The blurring caused by time passing confers an abstract quality to this image.
Fig.19 Left: 'Sugarflow'; Right: 'Coloured time'Conclusion
There is much to explore with radial spreads both scientifically and artistically. New photographic equipment has revealed new aspects to these forms, and my aim is to continue using this equipment in new ways to find new things. There are many materials waiting to be experimented with under different conditions, and, artistically, there is the excitement of participating in a fascinating and unpredictable natural process.
References
Burge, Pery ‘Hidden Patterns: creating radial spreads of ink in water’ Journal of Visualization , Vol.10 No.2: April 2007 pp.171-178.
Gasson, P.C. ‘Geometry of spatial forms’ Ellis Horwood Ltd 1983
Stewart, I. ‘What shape is a snowflake? Magical Numbers in Nature’ Weidenfeld&Nicolson, 2001
General References
Ball, P. ‘The Self-made tapestry Pattern formation in nature’ OUP,1999
Burgess, J., Marten, M., Taylor, R. ‘Microcosmos’ CUP, 1987