anchor.diff:        :markdown
           Here, $1+i$ is an eigenvalue and $(1, i)$ is an eigenvector. 
   
  -        Whenever a matrix has complex eigenvalues, the system it describes will spiral around $(0,0)$. To see this, drag $A$'s columns (the arrows) around until you get a spiral. The eigenvalues are plotted in the real/imaginary plane to the right. You'll see that whenever the eigenvalues have an imaginary part, the system spirals, no matter where you start things off.
  +        If a matrix has complex eigenvalues, its sequence spirals around $(0,0)$. To see this, drag $A$'s columns (the arrows) around until you get a spiral. The eigenvalues are plotted in the real/imaginary plane to the right. You'll see that whenever the eigenvalues have an imaginary part, the system spirals, no matter where you start things off.
   
       section(ng-controller="FourQuadCtrl")
         | steps:
  
positive.code:           fibonacci-sequence
  
          :markdown
            As you can see, the system goes toward the grey line, which is an eigenspace of the matrix.
  
            ###Markov Chains
  
            Suppose that, every year, a fraction $p$ of New Yorkers move to California and a fraction $q$ of Californians move to New York. Drag the circles to decide these fractions and the number starting in each state.
  
  
negative.code:           simple-plot
            p
              :markdown
                ###What are eigenvalues/vectors good for?
                Eigenvalues/vectors explain the behavior of systems that evolve step-by-step, where each step occurs as multiplication by a matrix $A$. If you keep multiplying $v$ by $A$, you get a sequence $\{ v, Av, A^2v,\}$ etc. As you can see below, eigenspaces attract this sequence and draw it toward $(0,0)$ or farther away, depending on their eigenvalues.
  
            div(ng-controller="PopulationCtrl")
              simple-plot
  
            p
              :markdown
                Let's explore some applications and properties of these sequences.
  
      section(ng-controller="BacteriaCtrl")
        p
          :markdown
            ###Fibonacci Sequence
            Suppose you have some amoebas in a petri dish. Every minute, all adult amoebas produce one child amoeba, and all child amoebas grow into adults (Note: this is not really how amoebas reproduce.). So if $t$ is a minute, the equation of this system is
  
          script(type="math/tex; mode=display").
              \begin{eqnarray} 
  