
Welcome to radio-active.co.uk My name is Eddy Crowley from hive-berry.com
This is a double spiral, golden ratio project, one spiral clockwise, the other anti-clockwise giving a radiowave zoom effect.
This is a double spiral, golden ratio project, one spiral clockwise, the other anti-clockwise giving a radiowave zoom effect.
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The golden ratio, often denoted by the Greek letter φ (phi), is an irrational number approximately equal to 1.6180339887. It arises from the solution to the equation x² = x + 1, where φ = (1 + √5)/2. This ratio appears frequently in nature, art, architecture, and mathematics due to its aesthetically pleasing properties and self-similar patterns.Golden Ratio Spirals. A single golden ratio spiral is a type of logarithmic spiral where the radius grows by a factor of φ with every quarter-turn (90 degrees). Mathematically, in polar coordinates, the equation for a logarithmic spiral is r = a * e^(bθ), where:
r is the radius,
θ is the angle,
a is a scaling factor,
b determines the tightness (for a golden spiral, b = (2/π) * ln(φ) ≈ 0.30635 to achieve the φ growth per full turn).
These spirals approximate the shapes seen in nautilus shells, galaxies, hurricanes, and even plant growth patterns like phyllotaxis.Double Spiral with Clockwise and Anti-Clockwise Directions. A double spiral extends this by combining two such spirals:
Clockwise spiral: Rotates in a right-handed direction (e.g., increasing θ positively, like a standard clock's hands).
Anti-clockwise (counter-clockwise) spiral: Rotates in a left-handed direction (e.g., increasing θ negatively or mirroring the first spiral).
When overlaid or interlaced, these opposing spirals can create symmetrical, dynamic visual effects. In the context of radio-active.co.uk's "radiowave zoom effect," this might refer to an optical illusion or animation where the spirals appear to pulse, expand, or mimic electromagnetic wave propagation (like radio waves), perhaps zooming in or out infinitely due to the self-similar nature of golden spirals. This could be inspired by fractal geometry or op-art, where the interplay of directions generates a sense of motion or radiation emanating from a central point.For example, imagine starting from a common origin:
The clockwise spiral expands outward in one direction.
The anti-clockwise spiral mirrors it, expanding in the opposite rotational sense. Together, they form a balanced, harmonious structure that avoids asymmetry, potentially evoking waves rippling in multiple directions
The design's concentric rings and curving spirals approximate a logarithmic spiral, which mathematically aligns with the golden ratio (φ ≈ 1.618), supporting the thread's speculation on a "divine ratio" through symmetrical, nature-inspired proportions seen in shells and galaxies.
Get in touch with me, Eddy Crowley on social media
'X' @Hive_Berry
x.com/Hive_Berry
Check here for background on this project :
Feel free to print off this project site and use the line drawing to fill and make own versions to post on @Hive_Berry on 'X' platform.