Golden Mean V04 By Drmolly Link -

The Golden Mean, also known as the Golden Ratio, is a mathematical concept that has fascinated philosophers, artists, and scientists for centuries. It is an irrational number approximately equal to 1.61803398875, often represented by the Greek letter phi (φ).

• Performance Optimisation – The code now runs at 60 fps on most browsers, even on mobile devices, thanks to a switch from draw()‑loop to requestAnimationFrame with off‑screen canvases.
• Dynamic Palette – Instead of a static colour set, drMolly introduced a palette generator that samples complementary hues from the golden angle (≈137.5°) on the colour wheel, guaranteeing harmonious yet varied visuals.
• Mathematical Depth – Each iteration of the spiral now uses the continued‑fraction representation of φ (i.e., [1;1,1,1,…]) to place points, subtly echoing the infinite nature of the ratio.

// Draw a short line segment each frame let x1 = radius * cos(angle); let y1 = radius * sin(angle); let x2 = (radius * scaleFactor) * cos(angle + TWO_PI / phi); let y2 = (radius * scaleFactor) * sin(angle + TWO_PI / phi); line(x1, y1, x2, y2); golden mean v04 by drmolly link

The Golden Mean is a philosophical concept that suggests that virtues are characterized by a mean or middle ground between two extremes: excess and deficiency. Aristotle argued that virtues are not found at the extremes, but rather at the midpoint between excess and deficiency. For example, courage is the mean between cowardice (deficiency) and recklessness (excess). This concept is often represented graphically as a spectrum with the mean in the center: The Golden Mean, also known as the Golden

Version 04 by Dr. Molly

• Light tokens (player-driven narrative nods)
• Shadow tokens (GM-introduced setbacks)

Virtue

| | Deficiency | Mean | Excess | | --- | --- | --- | --- | | Courage | (0, 0) | Courage (5, 5) | Recklessness (10, 10) | | Generosity | Stinginess (0, 10) | Generosity (5, 5) | Extravagance (10, 0) | | Honesty | Dishonesty (0, 0) | Honesty (5, 5) | Deceitfulness (10, 10) | Performance Optimisation – The code now runs at

1. Facial Aesthetics: The Golden Mean has been used to evaluate and achieve optimal proportions in facial features, such as the distance between the eyes, the shape of the nose, and the proportions of the face.
2. Body Shape: The Golden Mean has been applied to understand and achieve optimal body proportions, including the ratio of the waist to the hips, and the proportions of the limbs.
3. Dental Aesthetics: The Golden Mean has been used to evaluate and achieve optimal proportions in tooth shape, size, and arrangement.