Generate Koch snowflake, Sierpinski triangle, dragon curve, and custom IFS fractals with adjustable iteration depth and coloring.
Choose the Koch snowflake, Sierpinski triangle, dragon curve, or a custom iterated function system, then adjust the iteration depth and coloring to generate a fractal image. Each preset defines a particular geometric recursion, while a custom IFS describes repeated transformations of an initial set. The important surprise is that iteration depth is not a linear detail control: every additional step multiplies the number of geometric pieces, so a small increase can make the drawing substantially denser without making it an exact infinite fractal.
Each named preset follows its own replacement rule. One Koch refinement replaces every segment with four shorter segments. A Sierpinski refinement retains three half-scale corner triangles, while a dragon-curve refinement doubles the segment count through its folding pattern. Repeating the selected rule produces a finite approximation of the corresponding limiting shape.
A custom iterated function system represents a set through a family of transformations whose repeated images form a self-similar result. Contractive transformations are the usual choice because they converge toward a bounded attractor. Coloring changes how iterations, pieces, or regions are distinguished in the rendered image; it does not change the underlying geometric recursion.
No. Every displayed result has a finite number of segments, triangles, or transformed copies. A greater depth can resemble the limiting fractal more closely at the available display scale, but it remains an approximation. Past some depth, newly generated features may also be smaller than individual screen pixels and therefore cease to add visible information.
No. A stable bounded attractor is normally associated with a finite family of contractive transformations. Transformations that expand distances or send copies far apart need not settle into a bounded figure. Heavy overlap can also produce a solid-looking region rather than visibly separated self-similar pieces, even when the system is mathematically well defined.
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