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The Julia set for a complex number $c$ is the boundary between points that escape to infinity and those that remain bounded under iteration of: $$z_{n+1} = z_n^2 + c$$Each value of $c$ produces a different fractal. Connected Julia sets correspond to points inside the Mandelbrot set; disconnected “dust” fractals come from points outside. Controls: Click the Mandelbrot set (left) to choose $c$. Drag to pan, scroll to zoom the Julia set. ...

The Clifford attractor is a 2D strange attractor defined by the iterative map: $$ \begin{aligned} x_{n+1} &= \sin(a \cdot y_n) + c \cdot \cos(a \cdot x_n) \\ y_{n+1} &= \sin(b \cdot x_n) + d \cdot \cos(b \cdot y_n) \end{aligned} $$With parameters $a = 1.8$, $b = -1.9$, $c = 1.0$, $d = 1.5$, the system traces out intricate fractal structures. The image above was generated from 300 million iterations, rendered as a density histogram with logarithmic scaling to reveal the fine detail in regions where the trajectory lingers. ...

The time gates in Chrono Trigger have a distinctive swirling blue portal effect. This shader recreates that look using layered sine waves, procedural hash noise for texture, and a spiral distortion centered slightly off-axis. The color gradient shifts from deep blue at the edges through cyan to near-white at the peaks, with a soft vignette that fades the portal into darkness at the rim. ...