Firebird spiral
d/dx artd/dx art constructs mathematical beauty through precise geometry, layering eleven identical logarithmic spirals to create a rhythmic, rotating dance of form. This piece captures the 'miraculous' nature of the equiangular curve, where infinite inward turns occupy a finite space in a vibrant, fiery bloom.
Firebird spiral
d/dx art constructs mathematical beauty through precise geometry, layering eleven identical logarithmic spirals to create a rhythmic, rotating dance of form. This piece captures the 'miraculous' nature of the equiangular curve, where infinite inward turns occupy a finite space in a vibrant, fiery bloom.
35 × 28 cm · about ⅕ the width of a 3-seat sofa
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Firebird spiral
d/dx art
Art Analysis
From the artist, d/dx art
Shells, storms and galaxies often take the form of an equiangular, or logarithmic, spiral. So does Romanesque broccoli, but I hate broccoli. This is a set of 11 spirals, each with the same origin but successively rotated by 20 degrees. It's easy to describe this kind of spiral mathematically, not so easy in words. Perhaps the simplest way to say it is that if you were to draw a whole lot of straight lines radiating our from the origin, wherever the spiral crossed one of those lines it would be at the same angle to the line - strictly, its tangent would be at the same angle - hence 'equiangular'. The spiral has many fascinating qualities - so many that the famous mathematician Jacob Bernoulli nicknamed it 'miraculous spiral'. Among them is the fact that no matter how many turns you add, the overall shape never alters - just turn and shrink and you're back where you started. Then there is the fact that you can add an infinite number of turns going inwards but the distance from any point along the spiral to the origin is finite! Extra tags: maths, mathematics, spirals
Eleven Miraculous Spirals Rotating Toward a Finite Center
The composition is built upon the equiangular spiral, a shape found in the wild architecture of shells, storms, and galaxies. By rotating this specific curve at successive twenty-degree intervals from a shared origin, the artist creates a complex lattice that mimics organic growth without the mess of the natural world. Each line maintains a constant angle relative to the radii emerging from the center, a mathematical property that lends the work a sense of inevitable, calculated balance.
There is a philosophical depth to these eleven spirals, rooted in the principles that fascinated mathematician Jacob Bernoulli. Because the overall shape remains unchanged regardless of how many turns are added—simply shrinking or rotating back to its original state—the image possesses a self-similar quality that feels both expansive and contained. The work invites the viewer to trace the path toward the origin, contemplating the paradox of an infinite journey that exists within a defined, finite boundary.
The work utilizes the equiangular spiral where the curve's tangent maintains a constant angle to the polar radius, resulting in a mathematically precise form.
The piece translates the algebraic equation for the golden ratio into a visual language of nested geometric shapes.
By repeating and rotating the same graphic element eleven times, the composition achieves a sense of motion and structural harmony.
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