Nicholas Rawitscher's Videos (Grasshopper) - Grasshopper

KMeans clustering.

2019-05-22T23:02:04.873Z

This is the first Machine Learning implementation I did from a number of different learning algorithms I plan to implement within SharpMatter.
K-Means is a clustering algorithm that to seeks to learn from the properties of unlabelled data. K-Means aims to partition a given data set in to N clusters within a given property, each data element will belong to the cluster with the nearest mean. The algorithm uses an iterative technique until the data set reaches the desired N clusters (when clusters don't change). At each iteration step each data set is assigned to the cluster whose average mean has the least squared Euclidean distance , then after the new clusters are formed the new centroids are calculated and the process is repeated. The least squared Euclidean distance basically means how far apart the data elements are from each other. The typical set up is the number of n-dimensional vectors (data) to be clustered, K number of clusters and j number of iterations needed until convergence.

Physarum Polycephalum. Chemical trails

2019-05-22T22:54:48.412Z

Physarum Polycephalum.
Physarum Polycephalum, better known as “Slime Mould” is a single celled organism that can perform complex biological computations without any central controlling mechanism. Due to this property its computational abilities have become widely researched since the beginning of the 21st century. My initial studies were developed with SharpMatter and are based on Jeff Jones book “From Pattern Formation to Material Computation. Multi-Agent Modelling of Physarum Polycephalum ”. Specifically from chapter 3 -3.3. For a brief overview you can look at http://dx.doi.org/10.1162/art1.2010.16.2.16202
Each particle like agent is encoded with very simple rules of behaviour. The agents communicate and interact with each other through a “pheromone value” in the environment. Each agent can receive and modify the local values of the chemical through their 3 different sensors. Diffusion then helps to propagate the chemoattractant values through the environment. Depending on how each agent reads its environment different collective patterns emerge over time. The patterns formed are most of the times dynamic and adaptive to changing environmental conditions.
My further goal through this research is to be able to generate a tool which can be used for solving design problems.

Physarum Polycephalum

2019-05-22T22:52:49.440Z

Random Walkers in C#

2017-08-26T02:01:24.961Z

The random walker class was coded in C#, to further process the geometry Millepede was used to create an isosurface that wrapped the path curves of each individual walker.

C# - Edward Lorenz Strange Attractor - Chaos

2017-08-26T01:57:37.039Z

I decided to code Edward Lorenz Strange Attractor while my reading of Chaos, Making a New Science, by James Gleick. The code uses the standard constant variables defined by Lorenz on his 3 differencial equations that describe his attractor in a chaotic behavior when rho > 24.7. All the values of X =sigma(Y-X) *dt never repeat themselves through each moment in time making their distribution totaly random, we can see this at the end of the video with the linear graph. The beautiful thing is that even though the values of X are randomly distribuited over time, the result is a beautiful ordered shape, this in essence is the principal of chaotic systems. Or as James Gleick would say " chaotic systems embed hidden ordering principles"

X =sigma(Y-X)
Y= -X*Z+rho*X-Y
Z = X*Y-betta*Z

X = dx/dt -------> change of X over time
Y = dy/dt -------> change of Y over time
Z= dz/dt -------> change of z over time

rho = 28
betta = 3/8
sigma = 10

http://mathworld.wolfram.com/LorenzAttractor.html