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Why does a Lichtenberg figure look like lightning?Lightning is shaped by a natural law called Diffusion Limited Aggregation (DLA). The same law that shapes electrical discharges in air (lightning) also shapes electrical discharges in acrylic. This shape is a special type of geometric pattern called a fractal.
Benoit Mandelbrot is credited with the invention of "fractal" geometry which he named as a contraction of "fractional" because of its focus on fractured shapes.
Unlike classical regular geometric figures (lines, triangles, circles, squares, etc.), fractal patterns are irregular (tortuous) and are repeated at ever smaller scales (self-similar).
Classical geometric figures are composed of lines (1-dimensional), planes (2-dimensional), and solids (3-dimensional). Fractal figures are between dimensions, that is, they have fractional dimensions such as 1.3, or 2.4, instead of 1, 2, or 3.
Lichtenberg figures on a flat surface have a dimension typically between 1.5 and 2. Lichtenberg figures in a solid, have a dimension between 2 and 2.5.
Why does it look like a feather or a plant?There are many types of fractals. The DLA (Diffusion Limited Aggregation) type of fractal is responsible for the shape of lightning as well as the shape of some trees, ferns, feathers, coral, cracks, frost, and many other natural structures.