Mathematics, for me, is a spiritual practice. To engage in mathematical study is to travel into strange and mystical lands, to explore the very fabric of reality and illusion, and to uncover secrets which hold even deeper secrets within them.

When I set to work with an HB pencil, ruler and compasses, it is in a spirit of both discipline and playfulness. The connection of lines and circles on the paper can suddenly lead to three-dimensionality, or an unexpected glimpse into infinity. These images are given life with richly toned markers, gel pens and ink liners. I choose colours with the same combination of artistic freedom and mathematical precision that I use for the initial outline - creating an intricate and glimmering world.

If you'd like to learn more about any of the artwork featured here, the techniques and/ or philosophy surrounding it, please get in touch: karen@scarletfruit.com

There is great creative joy in deciding where and how to connect points and lines. In this piece, the architecture, ground and sky are geometrically aligned to one another.

The initial focus is the large equilateral triangle. Its criss-crossing straight lines create a 3D warp effect, a Reuleaux Triangle emerging from the illusory curve. The triangle’s left and right sides form a hypotenuse against the skyscrapers: the outermost cells of the triangle align with the skyscraper windows, vertex to vertex. The cells dwarf the windows, pushing the skyscrapers into the background. Moreover, the skyscraper sides open out at 90° from the triangle edge; its lines continue in the foreground, creating a pattern of advancing triangles and rhomboids.

I started with a circle, and played with it. I was curious to know what would happen if I connected point to point to point to point to point ... and so on. This finally transformed into a sphere, containing multitudinous triangles, quadrilaterals and arrows. And then I wondered: what if I extend the lines further, and turn the sphere into a planet, caught in a network of golden threads, glittering in space?

The "brokenness" of the sphere, with the fragments flying outwards, brings movement to the image. If it had remained whole, with every section neatly coloured and no shards, it would have been static and lifeless.

The viewer is left to ponder what lies outside the boundaries. Where does the golden net finish - and how?

What happens to a pattern when an element is omitted? And then another pattern is superimposed?

In this image, a circumference is divided into 12 equidistant points. Every point is connected to every other - apart from the point immediately opposite. For example, 12 o’clock is connected to 1, 2, 3 o’clock and so on… but not 6 o’clock. It is this exception which creates the hollow central dodecagon.

The torus is then split into colour sections: red, orange, yellow, green, blue, indigo, violet. While these sections differ in size and shape, the torus’s reflection symmetry (top/bottom; left/right) is maintained. Within each section, individual hues are arranged randomly.

The resulting effect is fragmented, glittering and crystal-like.

It began as two circles meeting in a bubble, each with carefully spaced vertical lines. These lines were then connected horizontally - and suddenly there was a corridor, extending forever. Intense blue shades shift to pale grey as they head to the unknown.

The trippy feel is heightened by mathematical instruments -set squares and protractors- falling into the corridor, as if sucked into a vacuum, a vortex, or an irresistible gravitational field.

Finally, there is disparity between our perception and what is really there. The set squares seem disproportionately huge - but only in relation to the corridor. And the initial impression is a chaotic mix of shapes; a closer look reveals the presence of ordered pattern and symmetry.

This combines several inspirations: the vibrancy of 1980s airbrush art, myth and dreamscape, and subtle disrupting of symmetry.

Its creation was intensely mathematical. Firstly, I trusted geometry to guide the drawing. The background spectra, upper and lower dome, desert horizon and pyramid – all are brought together by lines that connect point to specific point. Secondly, in the ‘mosaic’ areas I distributed individual colours for a desired overall hue, or illusion of depth. This is evident in the sand, where dark foreground gradually fades to paler background.

The angled spectrum in the centre suggests an almost-staircase. Deliberately flouting the rules of spacing in perspective drawing, it teasingly flits between the 2- and 3- dimensional.

The apparent complexity of this design derives from a conceptually simple process: connecting points on the x and y axes at regular intervals (1,0 to 0,9; 2,0 to 0,8; 3,0 to 0,7...), applying and reflecting this throughout the image in a consistent pattern. The result is an illusion of three-dimensionality, with a central area that looms from its squeezed surroundings.

The title “No Curve” draws attention to the underlying technique. Contrary to appearance, the curvature is an illusion: every line drawn is entirely straight.

As with some of my other work, this image explores sci-fi-inspired themes. The colour arrangement conveys the sense of a flashing console, squishing and jumping and struggling against weird gravitational forces.

Science fiction and mathematical exploration are profoundly connected. Especially intriguing is mathematical art which hints at a complex narrative beneath its surface. A 2D image, while technically motionless, might contain the tantalising promise of release from its static confines - with potential for backstory, movement and transformation.

This image started experimentally, with a zigzag that increased by a single unit at every turn. After tracing, reversing, superimposing, connecting the points and adding a mirror image beneath, what emerged -unexpectedly- was a crinkly sarcophagus, rich in symmetries and bizarre folds. On extending the left-right symmetry further, it became a sarcophagus-spacecraft, suspended in an improbable sky.

This is an A3 piece on watercolour paper: using Promarker, ink liner, gel pen and glitter nail varnish. It's one example of how I explore geometric possibilities -using ruler and compasses- to create vivid dreamscapes that are part abstract, part figurative. The division into colour sections, and the use of metallic gel pen to create a delicate net-like "webbing", add further sophistication, uniqueness and visual excitement. At the centre is an equilateral triangle, surrounded by a square in a pentagon in a hexagon in an octagon (sorry, but no heptagon!) in a decagon in a dodecagon. The vertices of the inner and outer polygons are connected in a strict pattern to create the web's structure. At the heart of the web, outlined in black, is the red-eyed spider - its form emerging ghostlike from the lines of its silk. The spider in this case did not create the web; the web created the spider.

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