A colorful Trifoil Knot

Some time ago I was looking for a cool way to visualize parametric equations and I started working on the the trefoil knot. It is the simplest example of a nontrivial knot and it can be defined with the following parametric equations:

After a while this snippet came out:

from numpy import linspace,pi,cos,sin
phi = linspace(0,2*pi,100)
x = sin(phi)+2*sin(2*phi)
y = cos(phi)-2*cos(2*phi)
z = -sin(3*phi)

from pylab import scatter,subplot,cm,show
from numpy import abs
s=abs(((y+3)+2)*10)
scatter(x,y,c=x,s=s,edgecolor='w',cmap=cm.gist_rainbow)
scatter(x/1.4,y/1.2,c=x,s=s,edgecolor='w',cmap=cm.gist_rainbow_r)
scatter(x/1.8,y/1.5,c=x,s=s,edgecolor='w',cmap=cm.gist_rainbow)
show()

So, here's my colorful version of the trifold knot:

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Discovering and Visualizing Patterns with Python!

This Refcard is a collection of code examples that introduces the reader to the principal Data Mining tasks using Python. In the RefCard you will find the following contents:

• How to import and visualize data.
• How to classify and cluster data.
• How to discover relationships in the data using regression and correlation measures.
• How to reduce the dimensionality of the data in order to compress and visualize the information it brings.
• How to analyze structured data with networkx.

Each topic is covered with code examples based on four of the major Python libraries for data analysis and manipulation: numpy, matplotlib,sklearn and networkx. Here is a preview of the first two pages:

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Odd-Even sort visualized

The Odd/Even sort is a sorting algorithm which uses the concept of the Bubble Sort to move elements around. Unlike Bubble sort, the Odd/Even sort compares disjointed pairs by using alternating odd and even index values splitting the sorting in different phases. We have that in the odd phase all the element with an odd index i are compared with the adjacent even index i+1 and in the even phase all the element with an even index i are compared with the adjacent odd index i+1. These two phases are repeated until no exchanges are required. This is a Python snippet that make us able to visualize the behavior of the algorithm:

def oddeven_anim(a):
 imgidx = 0
 x = range(len(a))
 sort = False; 
 while not sort:
  sort = True;
  for i in range(1,len(a)-1,2): # odd phase
   if a[i] > a[i+1]:
    a[i+1], a[i] = a[i], a[i+1]
    sort = False;
  for i in range(0,len(a)-1,2): # even phase
   if a[i] > a[i+1]:
    a[i+1], a[i] = a[i], a[i+1]
    sort = False;
  pylab.plot(x,a,'k.',markersize=6)
  pylab.savefig("oddevensort/img" + '%04d' % imgidx + ".png")
  pylab.clf()
  imgidx =  imgidx + 1

# run the algorithm
a = range(300)
shuffle(a)
oddeven_anim(a)

As in the other examples of sorting visualization in this blog, we have an image for each step of the algorithm. The following video have been produced joining all the images (here is explained how):