Lindenmayer Systems

X → F+[[X]-X]-F[-FX]+X
  • F means “draw forward”
  • − means “turn left by some angle”
  • + means “turn right some angle”.
  • X and Y mostly does not correspond to any drawing action and is used to control the evolution of the curve.
  • The square bracket “[“ corresponds to saving the current values for position and angle, which are restored when the corresponding “]” is executed.
variables : X F
constants : + − [ ]
start : X
rules : (X → F+[[X]-X]-F[-FX]+X), (F → FF)
angle : 30°
Fractal Plant (7 iterations)
variables : X Y
constants : F + −
start : FX
rules : (X → X+YF+), (Y → −FX−Y)
angle : 90°
Dragon Fractal (14 iterations)
constants : F + −
start : F
rules : F → FF-[-F+F+F]+[+F-F-F]
angle : 22.5°
Fractal Curve Tree (5 iterations)
variables : X Y
constants : F + −
rules : (F → ), (X → FX+FX+FXFY-FY-) , (Y → +FX+FXFY-FY-FY)
angle : 90°
Closed Fractal (4 iterations)

Penrose Tiling

Penrose tiling v1 ( 4 iterations )
Penrose tiling v2 ( 9 iterations )

Mandlebrot Sets

z(0) = z,    z(n+1) = z(n)*z(n) + z,    n=0,1,2, ...   
Mandlebrot Set

Random bits of Thoughtful Euphoria

Love podcasts or audiobooks? Learn on the go with our new app.

Recommended from Medium

Data Entry in Excel

Idavoll Network Partners with Kylin Network

The Missing Guide To Setting Up Google Cloud Service Accounts For Google BigQuery

Salesforce ADM-201 Administration Essentials for New Admins Exam Question Part 2

The Function that changed my mind

GitOps: how exactly to Ops your Git?

Need for a Common Language: A Reference Architecture for Medicaid

Installing Server 2016/2019 (Core) GUI Less with Proxmox

Get the Medium app

A button that says 'Download on the App Store', and if clicked it will lead you to the iOS App store
A button that says 'Get it on, Google Play', and if clicked it will lead you to the Google Play store
Venkkatesh Sekar

Venkkatesh Sekar

Random bits of Thoughtful Euphoria

More from Medium

Cell instance segmentation

Survey of No/Low Code AI End-to-end testing tools

Product developer’s guide to model training: Impute

The pitfalls of toy datasets