⠒⠰⡱⣡⠲⠱⡐⢀⠄⠄⠐⡐⠐⠄⢂⠆⠡⡀⠂⠄⠀⢠⠀⠂⠠⠐⡐⠔⠔⡐⠜⡐⠅⠰⢌⠆⡅⠐⠐⢄⠄⢂⠄⠠⡀⠀⠠⠀⠀⠀⠀⠀⠄⢎⢢⡣⡱⢬⢢⢜⠲⡱⠱ ⢂⢒⢌⠖⡒⡱⢀⢀⠄⡀⠁⠠⢂⠡⣈⠄⠀⠀⠀⢀⠄⡀⠄⢠⢂⡔⢈⡁⣂⠜⠜⠡⣁⠤⣂⠔⡰⡰⡐⡄⡄⠄⠄⡀⠐⠁⢂⠄⡀⠀⡀⠀⠀⠠⠀⠡⠃⢼⢆⠱⠦⡣⡌ ⠰⠰⣈⡌⠲⠂⠀⠄⢀⢀⠁⡐⡐⠀⢠⠀⠀⠀⡀⠄⠠⡰⠆⡍⢀⠆⢠⢂⣜⣼⣿⣿⣿⣿⣿⣿⣻⡽⣞⣜⡜⡜⢆⢆⢂⢄⠄⡀⡐⠀⠀⠀⠀⠀⠄⢀⠐⡜⢼⡩⡸⢣⢣ ⠢⠢⣘⡔⡔⠔⠀⠀⠀⠀⠀⢀⢀⡀⠀⠄⢀⠀⠄⠆⢆⠁⡐⠄⢄⢎⣞⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣟⣟⣽⢯⡹⣚⢼⡼⡢⡒⠔⠄⡀⠀⠀⠀⢀⠤⡸⢣⢣⢍⣚⡸⢦⢣ ⠆⢒⡑⡅⠲⡰⡰⢆⠱⡰⡡⢆⠤⣀⠠⡀⠀⠄⢌⢀⠄⢆⢁⢆⢧⣻⣻⣿⣿⣿⣻⣽⣽⣝⣍⠝⡽⡽⡽⣻⣟⡽⡹⡹⡭⡊⢂⢄⢂⠄⡀⢦⢎⠲⡣⡣⢪⢎⢜⡒⡱⣘⢆ ⢢⠒⡡⡑⠴⠲⡱⣅⢌⢢⢣⡡⡌⠀⠄⠂⡀⠤⠠⠰⠤⢀⠜⡜⣟⣟⣟⣿⡿⡿⣟⡝⣍⢎⡘⡹⡭⣫⢿⣿⣿⡿⡅⢀⠤⡠⠠⡐⢂⠂⠄⡇⢬⢎⢣⢣⢪⡊⡜⡜⡚⣘⢜ ⠆⠆⡱⡐⡔⡱⣉⡌⡌⠲⡡⣡⠀⠀⠀⢀⠐⠄⡐⠌⡰⡘⡜⣽⣟⣿⣿⣟⣯⣎⢦⣂⢰⢹⡳⣌⢯⣿⢿⣿⣿⣿⡲⡀⠠⢐⠅⠄⢂⠀⡐⠜⢬⢊⠖⠧⢪⢎⢜⢜⠒⡜⡜ ⠢⠒⡡⡡⢣⠲⠱⡡⠱⡱⠁⠠⢀⠠⠂⠄⠄⡀⠠⡘⡘⡧⣫⣟⢿⣿⣿⣿⣿⣿⣿⢿⣟⡽⣞⡽⣿⣿⣿⣿⣿⣿⣿⡆⢂⠆⢂⢂⢂⠂⠠⢢⢃⡜⢎⠧⡱⢣⡱⣘⠖⠜⡜ ⠦⠦⡱⡑⠥⢪⡒⣅⢢⠁⠀⢀⠄⠂⢀⢆⢆⡜⡞⣭⢞⢽⣻⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢯⢂⠒⡔⡔⡔⠄⠄⢂⢡⢘⢜⢎⢎⢎⠆⡎⢎⠜⢜ ⢢⢢⡑⡅⢢⠒⡰⡑⢌⢀⠀⢀⢀⣌⢣⢎⢞⢻⡽⡜⡽⣯⡿⣿⣿⣿⡿⣿⣿⣿⣿⣿⣿⣿⣿⣿⣿⢿⣻⢿⣿⣿⣿⣻⣂⠌⠆⠥⠢⢂⠄⠄⠤⣈⢎⢎⢚⢬⡒⡱⢆⠲⡘ ⠤⢢⢃⠣⢢⢢⢆⡅⢬⢃⢣⡱⡹⣞⢽⣹⢯⣏⢻⡝⡽⣻⣻⢿⣿⣿⢿⣟⡿⡿⡿⣿⣿⣿⣿⣿⣟⣽⣿⣿⣿⣿⣿⡿⣯⢢⠒⡌⢆⠂⡀⠄⢄⢂⡘⣌⠦⡱⡅⡱⢲⢒⠜ ⢆⠦⡱⡡⡒⢲⢡⠥⠲⡱⣱⢣⡹⡹⡼⣻⢯⢯⣹⢼⣹⣻⣿⣿⣿⣿⣿⣿⣻⢿⢿⣿⣿⣿⣟⣟⣽⣿⡱⣤⣦⢢⢏⢇⠣⢂⢆⠥⠢⠂⠠⢀⠄⠂⡈⢬⢆⡜⡜⡘⣌⢆⠲

Leonardo

Leonardo is a Python library that facilitates computation involving aestetic numeric relationships. At its core, it entails a façade to mathematical objects that are derived from the golden ratio, the silver ratio, or the bronce ratio. It aims to make visual computing easier by abstracting from the algebraic forms, allowing us programmers to reason about geometry at a higher order.

How to Use It

Constants

Leonardo embraces transcendental numbers that have aesthetic significance. These numbers are made accessible as constants in denoted namespaces. Each constant is foundational to a set of higher order concepts later explained.

Ratios

The geometric mean between any two numbers is a ratio. It establishes a relationship that carries aestetic qualities. The deliberate choice of a ratio, given some number, introduces a distinct aesthetic flavor to the composition with that number. The golden ratio is abundant in structures of natural growth, such as the human physis.

from leonardo import Gold, Silver, Bronce


str(Gold.ratio)
# 1.618

str(Silver.ratio)
# 2.414

str(Bronce.ratio)
# 3.303

I invite you to explore these relationships and their flavors in your compositions.

Angles

By applying the ratios to circles, we get a set of angles that carry related aesthetic properties and allow for other kinds of composition. The rotation by the golden angle constitutes a recurring principle in nature, found in the branching of trees, flower petals, and macroscopic structures of galaxies.

from leonardo import Gold, Silver, Bronce


str(Gold.angle)
# '137.51°'

str(Silver.angle)
# '105.44°'

str(Bronce.angle)
# '83.67°'

Working with Geometric Sequences

from leonardo import Gold


g = Gold() # g is a golden number

g17 = Gold(17) # g17 is a scaled golden number

g[-2:3] # prints the neighborhood of g
# [0.38196601125010515,
#  0.6180339887498948,
#  1.0,
#  1.618033988749895,
#  2.618033988749895]

# setting up fontsizes as a graphic designer
body, subheadline, headline = g17[-1:2]

body 
# 10.506577808748212

subheadline
# 17.0

headline
# 27.50657780874821

Make sure to read up on the silver and bronce ratio also, they are super cool.

Working with Sequences of Angles

A golden angle is an object with common units as properties.

from leonardo import Gold


Gold.angle
# Angle(fraction=0.38196601125010515)

[a.radians for a in Gold.angle_sequence[:5]]
# [2.399963229728653, 4.799926459457306, 7.199889689185959, 9.599852918914612]

[a.radians_canonic for a in Gold.angle_sequence[:5]]
# [2.399963229728653, 4.799926459457306, 0.9167043820063725, 3.316667611735026]

[a.degrees for a in Gold.angle_sequence[:5]]
# [137.50776405003785, 275.0155281000757, 412.5232921501135, 550.0310562001514]

[a.degrees_canonic for a in Gold.angle_sequence[:5]]
# [137.50776405003785, 275.0155281000757, 52.52329215011349, 190.0310562001514]

[a.fraction for a in Gold.angle_sequence[:5]]
# [0.3819660112501051,
# 0.7639320225002102,
# 1.1458980337503153,
# 1.5278640450004204]

[a.fraction_canonic for a in Gold.angle_sequence[:5]]
# [0.3819660112501051,
# 0.7639320225002102,
# 0.1458980337503153,
# 0.5278640450004204]

Gold.angle.complex
# (-0.7373688780783197+0.6754902942615238j)

x = Gold.angle.complex.real
x
# -0.7373688780783197

y = Gold.angle.complex.imag
y
# 0.6754902942615238

for angle in Gold.angle_sequence[:5]:
    p = angle.complex.real, angle.complex.imag
    print(p)
# (-0.7373688780783197, 0.6754902942615238)
# (0.08742572471695988, -0.9961710408648278)
# (0.6084388609788626, 0.7936007512916959)
# (-0.9847134853154287, -0.17418195037931164)

This is still an early version and no interfaces are guaranteed to stay stable.

Running Tests

Run the test-suite to see if the code base is behaving as expected.

python3 -m unittest