Link to originalThere are decades where nothing happens and there are weeks were decades happen - Lenin
Gradual quantitative changes are the base for qualitative jumps.
Vergleichsweise geringe Veränderungen können - sofern ein gewisser Druck aufgebaut wurde - als Katalysator für den Umschlag von Quantität in Qualität dienen.
“Great acts are made up of small deeds.” - Lao Tzu
Examples
- Water doesn’t just progressively get a little hotter or colder when supplying energy, it reaches different qualities (solid, liquid, gaseous, ).
- Ein Fass wird zum Überlaufen gebracht
Transclude of capital#^f0bee6
Link to originalCA's are cells arranged in space (classically discretized into a 1/2d grid) with (binary) states over which you apply low-complexity update rules in a convolution-like process (applied uniformly across space).
As you start adding a little bit of complexity to the definition of the CA—moving from binary states to larger state spaces, moving from 1D to 2D or 3D, making state continuous, making time continuous, make the update rules stochastic, using larger neighbourhoods, etc.—the behavior becomes incredibly complex (and often looking eerily life-like to us), even though the rules remain simple.
Fundamentally, you can think of CA’s as dynamical systems. You can model fluid-dynamics, chemical reactions, biological growth, etc. with them. But as you climb the hiearchy of abstraction layers, it makes sense to think about discrete agents interacting according to some rules (at which point the continuum gets lost—in the way it makes sense to model it anyway—, a qualitative leap).