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This article mainly explains "how to achieve the Sherbinsky triangle by Python". The content of the explanation is simple and clear, and it is easy to learn and understand. Please follow the editor's train of thought to study and learn "how to achieve the Sherbinsky triangle by Python".

Sherbinsky triangle

The sierpinskr triangle is also a fractal structure, the plane is called the Sherpinski triangle, and the three-dimensional one is called the Sherbinsky pyramid.

The Serpinski triangle is understood to be a given triangle, which is stacked in the shape of "pin". The triangle side of each degree is half the length of the original triangle.

White part: blank

Black part: spliced sierpinskr triangle

Degree: degree, number of times stacked

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The idea of Sherbinsky's triangle drawing

According to self-similarity, the Serpinski triangle is made up of three sierpinskr triangles halved in size in the shape of "product".

When the degree is limited (the number of stacking is limited), the triangles of degree=n are stacked by three triangles of degree=n-1 in the shape of "product". At the same time, the sides of the triangles of the three degree=n-1 are half the length of the triangles of degree=n. When degree=0, it can no longer be stacked

Size reduction: the triangle side length of degree=n-1 is half that of degree=n triangle.

Basic end condition: degree=0 (no more splicing)

Function parameter settings:

Points = {'left': (x, y),' top': (x, y), 'right': (x, y)}

Points is a dictionary that stores the coordinates of three points of a triangle. Each coordinate is another tuple.

Drawing order:

Draw the left triangle first

And draw a triangle.

Finally draw the triangle on the right.

Triangle drawing order:

First trace the left point of the triangle left

Retrace triangle vertices top

Finally, right, the right point of the triangle.

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Code

Running result:

Recursive understanding

Recursion can be understood as a loop, and if a recursive call is followed by a program, it can be understood as the nesting of a loop. At the end of the current recursive loop, the program jumps to the upper loop of the basic end condition to continue with the rest of the program

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