diff --git a/PCP_06_complex.ipynb b/PCP_06_complex.ipynb
index 7f0fbda..42cffb5 100644
--- a/PCP_06_complex.ipynb
+++ b/PCP_06_complex.ipynb
@@ -545,8 +545,8 @@
"
\n",
" - Model the Mandelbrot set as a binary indicator function $\\chi:\\mathbb{C}\\in\\{0,1\\}$, where $\\chi(c)=1$ if $c$ belongs to the Mandelbrot set and $\\chi(c)=0$ otherwise.
\n",
" - Only consider complex numbers $c=a+ib$ on a discrete grid on a bounded range. It suffices to consider the range $a\\in[-2,1]$ and $b\\in[-1.2,1.2]$. Furthermore, for efficiency reasons, use a grid spacing that is not too fine. First, try out $\\Delta a = \\Delta b = 0.01$. To create the grid, you may use the function
np.meshgrid
. \n",
- " - Test for each $c=a+ib$ on that grid, if $(v_c(k))_{k\\in\\mathbb{N}}$ remains bounded or not. Computationally, this cannot be tested easily. However, usually, the sequence $(v_c(k))$ increases in an exponential fashion in the case that it is not bounded. Therefore, a pragmatic (yet not always correct) test is to fix a maximum number of iterations (e.g., $K = 50$) and a threshold (e.g., $L = 100$). In case that $v_c(K)\n",
- "
- Plot $\\chi$ using the function
np.imshow
, use the colormap 'gray_r'
. Furthermore, use the parameter extent
to adjust ranges of the horizontal axis $[-2,1]$ (real part) and vertical axis $[-1.2,1.2]$ (imaginary part). \n",
+ " - Test for each $c=a+ib$ on that grid, if $(v_c(k))_{k\\in\\mathbb{N}}$ remains bounded or not. Computationally, this cannot be tested easily. However, usually, the sequence $(v_c(k))$ increases in an exponential fashion in the case that it is not bounded. Therefore, a pragmatic (yet not always correct) test is to fix a maximum number of iterations (e.g., $K = 50$) and a threshold (e.g., $L = 100$).
\n",
+ " - Plot $\\chi$ using the function
plt.imshow
, use the colormap 'gray_r'
. Furthermore, use the parameter extent
to adjust ranges of the horizontal axis $[-2,1]$ (real part) and vertical axis $[-1.2,1.2]$ (imaginary part). \n",
"
\n",
""
]
@@ -593,7 +593,7 @@
"metadata": {
"anaconda-cloud": {},
"kernelspec": {
- "display_name": "Python 3",
+ "display_name": "Python 3 (ipykernel)",
"language": "python",
"name": "python3"
},
@@ -607,7 +607,7 @@
"name": "python",
"nbconvert_exporter": "python",
"pygments_lexer": "ipython3",
- "version": "3.9.17"
+ "version": "3.9.18"
}
},
"nbformat": 4,