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     "execution_count": 4,
     "metadata": {},
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    }
   ],
   "source": [
    "using Plots\n",
    "pyplot(leg=false, size=(500,300))\n",
    "\n",
    "n = 10\n",
    "y = rand(n)\n",
    "vx, vy = randn(n), randn(n)\n",
    "\n",
    "quiver(y, quiver=(vx,vy))"
   ]
  },
  {
   "cell_type": "code",
   "execution_count": 5,
   "metadata": {
    "collapsed": false
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   "source": [
    "e(x,y) = exp(-x^2-y^2)\n",
    "f(x,y) = x * e(x,y)\n",
    "x = -2:0.2:2\n",
    "contour(x,x,f, xlim=(-2,2), ylim=(-2,2), fill=true)"
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   "cell_type": "code",
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   "source": [
    "# take the derivative, then scale down\n",
    "df(x,y) = P2(e(x,y) + x * e(x,y) * (-2x), x * e(x,y) * (-2y)) / 4\n",
    "\n",
    "# get a grid of points as a vector\n",
    "pts = vec(P2[(x[i],x[j]) for i=1:length(x), j=1:length(x)])\n",
    "\n",
    "# add the quiver plot\n",
    "quiver!(pts, quiver=df, marker=(:none,stroke(2,0.3)))"
   ]
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   "cell_type": "code",
   "execution_count": null,
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