Figurate Numbers

Figurate Numbers is the most comprehensive and specialized library for figurate numbers, developed in Ruby to date. It implements 241 infinite number sequences inspired by the groundbreaking work Figurate Numbers by Elena Deza and Michel Deza, published in 2012.

Install it from the gem repository:

gem install figurate_numbers

Figurate Numbers implements 241 infinite sequences using the Enumerator class in Ruby, each categorized by its geometric dimension. It is ideal for use in mathematical modeling, algorithmic composition, and integration with tools like Sonic Pi.

The sequences are organized following the structure of the Figurate Numbers book:

• 🟦 PlaneFigurateNumbers: 79 sequences (2D)
• 🟥 SpaceFigurateNumbers: 86 sequences (3D)
• 🟨 MultiDimensionalFigurateNumbers: 70 sequences (4D and beyond)
• 🧬 Zoo of figurate-related numbers: 6 additional sequences (included in the MultiDimensional module)
• ⚙️ ArithTransform: p-adic transformations and other arithmetic operations

require 'figurate_numbers'

## Using take(integer)
FigurateNumbers.pentatope.take(10)

## Storing and iterating
f = FigurateNumbers.centered_octagonal_pyramid
f.next
f.next
f.next

Starting from version 1.5.0, figurate_numbers not only supports global access via FigurateNumbers and the use of specific classes for separate access, but also introduces new p-adic transformations and other mathematical operations that can be applied directly to sequences.

PlaneFigurateNumbers.polygonal(19)
SpaceFigurateNumbers.rhombic_dodecahedral
MultiDimensionalFigurateNumbers.six_dimensional_hyperoctahedron
seq = MultiDimensionalFigurateNumbers.five_dimensional_hypercube.take(15)
ArithTransform.ring_padic_val(seq, 3)

📚 Explore the detailed list of figurate numbers and arithmetic transformations here 🔍.

Simply copy the entry point path from the lib/figurate_numbers.rb file where the gem is installed.

require "<PATH>"

pol_num = FigurateNumbers.polygonal(8)
350.times do
  play pol_num.next % 12 * 7  # Some mathematical function or transformation
  sleep 0.125
end

amp_seq = SpaceFigurateNumbers.centered_hendecagonal_pyramidal
100.times do
  sample :bd_sone, amp: ArithTransform.padic_norm(amp_seq.next, 3) # p-adic amplitude control
  sleep 0.25
end

The main change introduced after version 1.3.0 is that you must now import the file using require instead of run_file; otherwise, it will not function.

See discussion in the Sonic Pi community thread right here!

Explore the complete list of figurate number sequences:

• View all implemented methods and sequences 🔍

Corrections to formulas and data found in Figurate Numbers (2012):

• See full list of known errata 🔍