Author: elkingtowa

Kudzu

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kudzu

Kudzu is an invasive plant that grows overs trees and other plants. This weed sprawls so widely that it kills other plants by shading them from the sun.

Joshua Elkington

Harvard College

Hacking is Learning

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Hacking is doing something without any prior knowledge of the skills required to do the thing. A programmer is a hacker if they promise something in a certain language or a certain framework they have no idea how to use. But through the process of hacking, the programmer will learn the language and framework. Hacking at stuff is a way to gain skills and knowledge. However, there is a big possibility that bad habits can form. So it’s important to reach out to experts if you run into trouble. Don’t be afraid to enter the unknown and hack. Its OK to break things.

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Joshua Elkington

Harvard College

Lorenz Attractor

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The Lorenz attractor is a set of chaotic solutions to the system of ordinary differential equations called the Lorenz equations. The plot of the attractor resembles a butterfly.

Python code:

#Lorenz Attractor
#http://journals.ametsoc.org/doi/abs/10.1175/1520-0469%281963%29020%3C0130%3ADNF%3E2.0.CO%3B2

import numpy as np
import matplotlib.pyplot as plt
from mpl_toolkits.mplot3d import Axes3D

def lorenz(x, y, z, s=10, r=28, b=2.667) :
x_dot = s*(y – x)
y_dot = r*x – y – x*z
z_dot = x*y – b*z
return x_dot, y_dot, z_dot

dt = 0.01
stepCnt = 10000

#initial values
xs = np.empty((stepCnt + 1,))
ys = np.empty((stepCnt + 1,))
zs = np.empty((stepCnt + 1,))
xs[0], ys[0], zs[0] = (0., 1., 1.05)

for i in range(stepCnt) :
#ODE system
x_dot, y_dot, z_dot = lorenz(xs[i], ys[i], zs[i])
xs[i + 1] = xs[i] + (x_dot * dt)
ys[i + 1] = ys[i] + (y_dot * dt)
zs[i + 1] = zs[i] + (z_dot * dt)

fig = plt.figure()
ax = fig.gca(projection=’3d’)
ax.plot(xs, ys, zs)
ax.set_xlabel(“X Axis”)
ax.set_ylabel(“Y Axis”)
ax.set_zlabel(“Z Axis”)
ax.set_title(“Lorenz Attractor”)
plt.show()

Joshua Elkington

Harvard College