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Category Archives: fractals
Draw a Pythagoras tree fractal in C#
A Pythagoras tree (or Pythagorean tree) is a fractal tree built from squares. It starts with a square that forms the tree’s base. The program then makes the Pythagoras tree by recursively attaching two smaller branches to the original branch. … Continue reading
Posted in drawing, fractals, graphics, recursion
Tagged C#, C# programming, drawing, example, example program, fractals, graphics, Pythagoras tree, Pythagorean tree, recursion, Windows Forms programming
1 Comment
Draw a Sierpinski pentagon in C#
In a Sierpinski pentagon, larger pentagons are recursively divided into five smaller pentagons with a sixth uncolored pentagon in the center. The following picture shows the first four levels of the resulting fractal. For this example, I decided to think … Continue reading
Posted in drawing, fractals, graphics, recursion
Tagged C#, C# programming, drawing, example, example program, fractals, graphics, recursion, recursively, Sierpinski pentagon, Windows Forms programming
2 Comments
Draw a Fibonacci word fractal in C#
This example uses the Fibonacci word to draw a fractal curve. For information on the Fibonacci word, see the post Calculate Fibonacci words in C#. To draw a curve with level N, use Fibonacci word number N. Loop through the … Continue reading
Posted in algorithms, fractals, graphics, mathematics
Tagged algorithms, C#, C# programming, example, example program, Fibonacci, Fibonacci fractal, Fibonacci numbers, Fibonacci word, Fibonacci word fractal, Fibonacci words, fractals, graphics, iterated equation, mathematics, Windows Forms programming
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Calculate Fibonacci words in C#
You can find Fibonacci words by concatenating previous Fibonacci words much as you calculate the Fibonacci sequence by adding previous values in the sequence. The first two Fibonacci words are: S0 = 0 S1 = 01 The following Fibonacci words … Continue reading
Posted in algorithms, fractals, graphics, mathematics
Tagged algorithms, C#, C# programming, example, example program, Fibonacci, Fibonacci sequence, Fibonacci words, fractals, graphics, mathematics, Windows Forms programming
1 Comment
Draw the Weierstrass function in C#
The Weierstrass function was discovered by Karl Weierstrass in 1872. It’s an odd function that is continuous everywhere but differentiable nowhere. I’ll explain what that means shortly. Here’s the function: Here: The following two sections explain what it means to … Continue reading
Posted in algorithms, drawing, fractals, graphics, mathematics
Tagged algorithms, C#, C# programming, continuous function, differentiable function, discontinuous function, drawing, example, example program, fractals, graphics, mathematics, nondifferentiable function, Weierstrass curve, Weierstrass function, Windows Forms programming
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Draw a recursive overlapping snowflake fractal in C#
The example Draw a recursive snowflake fractal in C# explains how to use an iterator and a generator to draw a snowflake fractal. This example uses the same technique with the initiator and generator shown in the second and … Continue reading
Draw a recursive von Koch snowflake fractal in C#
This example shows how to draw a von Koch snowflake fractal. It uses the same techniques described in the post Draw a recursive snowflake fractal in C#. The DrawSnowflake and DrawSnowflakeEdge methods are exactly the same as before. The … Continue reading
Posted in algorithms, drawing, fractals, graphics, mathematics
Tagged algorithms, C#, C# programming, drawing, example, example program, fractals, generator, graphics, initiator, mathematics, recursion, recursive, snowflake, snowflake curve, snowflake fractal, von Koch, von Koch fractal, von Koch snowflake, Windows Forms programming
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Draw a recursive snowflake fractal in C#
This program draws a recursive snowflake fractal by using an initiator and a generator to define the fractal’s shape. The initiator is a curve that represent the fractal’s basic shape. In this case, the initiator is the triangle shown … Continue reading
Draw a curly tree fractal using less memory in C#
To draw trees, the example Draw a curly tree fractal in C# first builds lists holding the end points of the tree’s branches. It then finds the bounds of those points, makes a transformation to center the tree nicely, and … Continue reading
Posted in algorithms, drawing, fractals, graphics, mathematics
Tagged algorithms, C#, C# programming, curly tree, curly tree fractal, drawing, example, example program, fractals, graphics, mathematics, recursion, tree, tree fractal, Windows Forms programming
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Draw a curly tree fractal in C#
This example uses recursion to build a fractal tree. It starts by drawing the tree’s trunk. At the end of the trunk, it creates two branches. At the end of each branch, it creates two new branches A and B. … Continue reading
Posted in algorithms, drawing, fractals, graphics, mathematics
Tagged algorithms, C#, C# programming, curly tree, curly tree fractal, drawing, example, example program, fractals, graphics, mathematics, recursion, tree, tree fractal, Windows Forms programming
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