#!/usr/bin/env python
# coding: utf-8

# Kuramoto-Sivashinsky equation (KSE)
# =================
# 
# KSE is a representative example of spatio-temporal chaos [1].
# 
# $$
# \frac{\partial u}{\partial t}
# + u \frac{\partial u}{\partial x}
# + \frac{\partial^2 u}{\partial x^2}
# + \frac{\partial^4 u}{\partial x^4}
# = 0
# $$
# 
# [1]: http://www.springer.com/us/book/9783642696916

# In[1]:


get_ipython().run_line_magic('matplotlib', 'inline')
import pandas as pd
import matplotlib.pyplot as plt


# In[2]:


get_ipython().system(' cat examples/kse.rs')


# In[3]:


get_ipython().system(' cargo run --release --example kse > kse.csv')


# In[4]:


df = pd.read_csv("kse.csv", header=None).set_index(0)


# In[5]:


plt.figure(figsize=(10, 10))
plt.imshow(df, interpolation="bilinear")
plt.ylabel("time", fontsize=20)
plt.savefig("kse.png")