Holomorphic Function Explorer
In this webapp you can play with functions from ℂ to ℂ and their
derivatives. Draw with your mouse on the left side and see your
transformed drawing on the right side!
You can input a complex function with one variable 𝑧, all the
regular operators such as
+ - * / ^,
re(),
im(),
sqrt() and
abs()
are suppored. In general, we support anything that math.js can
parse.
Make sure to adjust the zoom level on each side for the perfect experience.
As you mouse over the graph, the complex derivative will be
displayed as a 2D linear transformation with red and green
arrows for the basis. Check for youself that:
- If you draw around the derivative the drawing will be transformed pretty linearly.
- The derivative preserves angles! Cauchy-Riemann FTW.
Functions without derivatives
If you input a function without complex derivatives, such as e^z+re(z),
we will "approximate" the derivative by treating the function as ℝ²🠂ℝ².
Then you can see for yourself how the Cauchy-Riemann equations
break down as the derivative no longer preserves angles.
Cool functions to try
e^ze^z+re(z)(z+2)^2(z-1-2i)(z+1)sqrt(z)log(z)*re(z)z*(abs(re(z))+abs(im(z)))
If you find any interesting functions please let me know.