EFFULGENT @complex-objects-blog - Tumblr Blog

Visualization of dynamic vector field. At each point the components of the vector was defined in terms of polar coordinates (rho, theta). I allow radially propagating waves (like a circular ripple on water) to define the rho and theta components. As the waves move outward the vector components change, leading to interesting patterns.

#polar coordinates #vector field

Plotting the surface W1 - W2 = 0 for two time-dependent functions defined over R^3 in spherical coordinates.

W1(rho,phi,theta,t)=sin(rho*theta*t)

W2(rho,phi,theta,t)=t*sin(phi)

#spherical functions #high dimensional

Implementing Schelling’s segregation model / homophily in Matlab. Red and green individuals are selected at random and moved to the nearest vacant location which satisfies a certain “good neighborhood” criterion. Basically, an individual tries to move to locations where there is more of her own type present than the opposite type. Over time, we observe an emergent segregation and pattern formation.

#homophily #segregation model #abm #agent based modeling

Top: a very small image with square lattice. Blue crosses show the centers of 3x3 subimages. I represent each subimage as a 9-dimensional image vector. Then I use kernel PCA to embed the vectors into 3D (Bottom). The lines show adjacency within the original square lattice. A very interesting and non-obvious topology can be seen relating the image vectors.

I used k-means clustering of the pixels (converted to L*a*b colorspace) to segment the beans image into five groups Each group is shown below. I only used values in the “a” and “b” layers during clustering; so it’s clustering in a 2D colorspace.

#image processing #image segmentation

Top: image of Turing pattern. Bottom: I took overlapping square subimages arranged in a rectangular lattice covering the image. Each subimage was represented as an image vector. LLE (a dimensionality reduction procedure) was used to embed these vectors in 3D. Lines show connections within the 2D lattice. Points represent individual subimages.

#dimensionality reduction #computer vision