# Pattern Formation ![globe](images/earth.jpg) ### From a homogeneous state to structure
## Example: Ripples ![globe](images/sand2.png) ![globe](images/sand1.tiff) These stripes and patches form by an amplification of small perturbations by laminar wind / water flow across the surface.
## Morning Glory
[Morning Glory is a cloud phenomenon](https://en.wikipedia.org/wiki/Morning_Glory_cloud) that exhibits long regular rotating rolls with regular spacing. They are a rare meteorological phenomenon.
## fractal, self-similar patterns ![globe](images/river.png) This sattelite image of a river system exhibits fractal / self-similar geometry.
## Bernard Convection
When a thin film of oil in a pan is heated from below the heat gradient is too large for heat dispersion to distribute the heat. As a result convection cells emerge that transport heat from below to the surface.
## Belousov–Zhabotinsky reaction ![sync](images/bz1.png) ![sync](images/bz2.png) The BZ reaction is an activator-inhibitor systems that exhibits oscillatory behavior in a well mixed container.
## Belousov–Zhabotinsky reaction
The [BZ reaction](https://en.wikipedia.org/wiki/Belousov%E2%80%93Zhabotinsky_reaction) in a thin film on a petri-dish exhibits characteristic target patterns and spiral waves. It's one of the most famous systems known to exhibit this behavior.
## Dictyostelium discoideum ![sync](images/dicty.png)
The organism [Dictyostelium discoideum](https://en.wikipedia.org/wiki/Dictyostelium_discoideum) is an amoeba, a slime mold that exhibits interesing behavior. In one mode it has a single cell life-style. When food runs out the cells signal to their environment and aggregate, form a multi-cellular organism and cells differentiate.
## Dictyostelium discoideum ![sync](images/dicty.png)
This video shows the dynamics of the **signaling molecule cAMP** that Dictyostelium discoideum uses to aggregate. When individuals are exposed to cAMP the move up the cAMP gradient and excreet cAMP themselves.
## Pattern Formation in the brain ![sync](images/brain.jpg) Optical pathways in the brain. Each eye splits the visual field into left/right hemispheres. The axonal fibers from each of the two eyes and two hemispheres get distributed to the left/right visual cortices in the back of the brain, such that the left visual cortex receives information from the left visual field (from both eyes) and the right visual cortex from the right visual field.
## Orientation maps in the visual cortex ![sync](images/orientation.png) Some cells in the visual cortex exhibit an orientation preference, they respond primarily to visual stimuli on the retina that are oriented in a specific direction. When the entire visual cortex is mapped and the orientation preference mapped in color for many species we see an orientation map. This map exhibits characteristic pinwheels, singularities in the orientation preference.
## Ocular Dominance Maps ![sync](images/ocular.jpg) Likewise, cells in the visual cortex exhibit an ocular dominance. They exhibit the tendency to respond to stimuli presented to one eye more than those presented to the other eye. As a function of location on the visual cortex the ocular dominance patterns consists of stripes of a specific wave-length.
## Patterns on Snails and Shells ![sync](images/snails.png) ![sync](images/shellbook.png) Some species of snails and sea shells exhibit complex patterns on their surface. How these emerge and can be classified is discussed in a grear book by [Hans Meinhardt]( https://de.wikipedia.org/wiki/Hans_Meinhardt ): [The Algorithmic Beauty of Sea Shells](https://www.amazon.de/Algorithmic-Beauty-Shells-Virtual-Laboratory/dp/3540921419/ref=sr_1_1?ie=UTF8&qid=1529839438&sr=8-1&keywords=the+algorithmic+beauty+of+sea+shells).
## Animal Coats ![sync](images/fur.png) One of the most prominant examples of pattern formation in biology are patterns on animal coats. Typically they come in stripes or semi-regular patches.
## Embryogenesis ![sync](images/embryo.png) The most sophisticated phenomenon of pattern formation is embryogenesis which can be understood as a sequence of pattern forming events that gain more and more complexity. The image depicts the embryo of a bat.
## Embryogenesis ![sync](images/urchin.png) A famous example that clearly showed that the shape of the organism isn't hardcoded but rather a sequence of pattern forming events is illustrated above experimenr in which the early embryo (two cells) is split. Each of the halfs then develops a full sea urchin larvae (a smaller version though).
## Morphogenesis and Gene Regulation ![sync](images/gene1.png) ![sync](images/gene2.png) The way this is accomplished? In morphogenesis genes that are play a role in the process regulate each other and eventually are expressed in a spatially inhomogeneous pattern. For example in the embryo of the fruitfly different genes are expressed in stripes across the embryo which eventually leads to the segmentation of the embryo.
## Morphogenesis in the Fruitfly Embryo
This video shows the development of a fruitfly embryo in toto.
## Digits and the Turing Mechanism ![sync](images/digits.png) This image was taken from the paper [_Hox Genes Regulate Digit Patterning by Controlling the Wavelength of a Turing-Type Mechanism_](http://science.sciencemag.org/content/338/6113/1476) that shows that the digit development is driven by the Turing Mechanism, one of the key mechanisms in which patterns self-organize from a homogeneous states.
## Patterns in Collective Behavior ![sync](images/microbe-pattern.png) Patterns also appear in collective behavior in colonies of microbes.
## Alan Turing & the Turing Mechanism ![sync](images/turing.tiff) ![sync](images/turing-paper.png) An important mechanism that we will discuss in class was discovered by [**Alan Turing**](https://en.wikipedia.org/wiki/Alan_Turing) and published in the above paper. It's a seminal paper on the topic and was very important for understanding how patterns may emerge in biological systems.