Interactive simulations & visualizations
Visualizing the beauty in physics and mathematics
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Divergence and curl demo
What are you looking at?
This is a dynamic particle and vector field simulation where points interact with
sources, sinks, and swirling currents. Every particle moves according to the
invisible forces around it, tracing the flow of this small, colorful universe.
🎯 Intuitive understanding of the divergence and curlOriginal idea by Let's code physics VPython demo is available as well, see div_curl_demo.py
Click to start the animation!
Scalar vis-à-vis vector quantities
This excellent visual guide originates from
House of Physics .
\[\text{Divergence: }\vec{\nabla} =\begin{pmatrix} \partial/\partial x \\ \partial/\partial y \\ \partial/\partial y \end{pmatrix} \Rightarrow \vec{\nabla} \cdot \vec{V} = \dfrac{\partial V_x}{\partial x} + \dfrac{\partial V_y}{\partial y} + \dfrac{\partial V_z}{\partial z}\]
\[\text{Curl: } \vec{\nabla} \times \vec{V} = \begin{vmatrix} \hat{x} & \hat{y} & \hat{z} \\ \dfrac{\partial}{\partial x} & \dfrac{\partial}{\partial y} & \dfrac{\partial}{\partial z} \\ V_x & V_y & v_z \end{vmatrix} = \begin{pmatrix} \partial V_z/\partial y - \partial F_y/\partial z \\ \partial V_x/\partial z - \partial F_z/\partial x \\ \partial V_y/\partial x - \partial F_x/\partial y\end{pmatrix}\]
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