Collection: Lorenz System

The Lorenz system is a system of ordinary differential equations first studied by Edward Lorenz and, a meteorologist, around 1963. It was derived from a simplified model of convection in the earth’s atmosphere. It also arises naturally in models of lasers and dynamos. The system is most commonly expressed as 3 coupled non-linear differential equations:
  • dx / dt = a (y – x)
  • dy / dt = x (b – z) – y
  • dz / dt = xy – c z

It is notable for having chaotic solutions for certain parameter values and initial conditions. In particular, the Lorenz attractor is a set of chaotic solutions of the Lorenz system.

In popular media the ‘butterfly effect’ stems from the real-world implications of the Lorenz attractor, i.e. that in any physical system, in the absence of perfect knowledge of the initial conditions (even the minuscule disturbance of the air due to a butterfly flapping its wings), our ability to predict its future course will always fail. This underscores that physical systems can be completely deterministic and yet still be inherently unpredictable even in the absence of quantum effects.

The shape of the Lorenz attractor itself, when plotted graphically, may also be seen to resemble a butterfly.

8 products
  • Lorenz Men's T-shirt
    Regular price
    from $36.50 USD
    Sale price
    from $36.50 USD
    Regular price
    Unit price
    per 
    Sold out
  • Lorenz Bean Bag Chair Cover
    Regular price
    $70.00 USD
    Sale price
    $70.00 USD
    Regular price
    Unit price
    per 
    Sold out
  • Lorenz Flip-Flops
    Regular price
    $18.00 USD
    Sale price
    $18.00 USD
    Regular price
    Unit price
    per 
    Sold out
  • Lorenz Men's Rash Guard
    Regular price
    from $46.00 USD
    Sale price
    from $46.00 USD
    Regular price
    Unit price
    per 
    Sold out
  • Lorenz Premium Pillow
    Regular price
    from $26.50 USD
    Sale price
    from $26.50 USD
    Regular price
    Unit price
    per 
    Sold out
  • Lorenz White glossy mug
    Regular price
    from $11.00 USD
    Sale price
    from $11.00 USD
    Regular price
    Unit price
    per 
    Sold out
  • Lorenz Laptop Sleeve
    Regular price
    from $25.00 USD
    Sale price
    from $25.00 USD
    Regular price
    Unit price
    per 
    Sold out
  • Lorenz Canvas
    Regular price
    from $42.00 USD
    Sale price
    from $42.00 USD
    Regular price
    Unit price
    per 
    Sold out