MetaLegendre

For My 26th Sketch of Mathober2025, MetaLegendre is coded with SonicPi & Desmos. For the 11th Prompt of Orthogonal Polynomial, uses a desmos sketch that half of the Legendre Polynomials are in 2D and the other half are in 3D. For the 27th Prompt of Bidiminished, the sound is control by the volume of a Metabidiminished Icosahedron.

Poetry

Graphing
Through the Volume
Do the Patterns Resume?
As they await their crafting

Video

Code

SonicPi (Sped Up 2.2x)

#https://mathworld.wolfram.com/MetabidiminishedIcosahedron.html

#The volume of a Metabidiminished Icosahedron is represented with V
#The audio plays out the bidiminished


V = (1.0 / 6) * (5 + 2 * Math.sqrt(5))

def metabidi(units)
  vol = V * units
  return vol
end



live_loop :volume do
  use_random_seed Time.now.to_i / metabidi(2)
  with_fx :ping_pong do
    use_bpm metabidi(rrand_i(45,78))
    sample [:drum_bass_hard,:tabla_ghe2,:guit_em9].choose,beat_stretch: metabidi(dice(5)) , rate: metabidi(dice(3)), sustain: metabidi(dice(4))
  end
  sleep [metabidi(0.5),metabidi(0.75),metabidi(0.97)].choose
end

Desmos