Spirograph toy that is used to produce complex patterns using plastic cogs and colored pens. A fractal is a curve, that is developed using a recurring pattern that repeats itself infinitely on a low scale. Fractals are used for modeling structures (such as snowflakes) or for describing partly chaotic phenomena.
Spirograph can be used to draw various fractals. Some of them are given below
You can visit benice-equation-blogspot.in for more fractals design with there parametric equation. Some of them are given below
Mathematics behind the curtain
These are the two parametric equation to form a spirograph fractals, to understand these equations you have to consider a generalized figure of spirograph.
For the mathematics part you can refer to Wiki although i’ll try to explain a little of that mathematics in a short here. If we are interested behind the maths then you can check out the referred links. So as of now, these various curve can be drawn by using a parametric equation and varying some values of that equation we can get different fractals. So here’s the parametric equation:
R is a scaling parameter and does not affect the structure of the Spirograph.
So, now let’s try to implement this in code.
The above program draws 4 different kinds of spirograph fractals, try to generate other fractals and then upload your github links in the comment. I’ll be happy to help you out if any error comes up.
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