Category Archives: fractals

Draw a Pythagoras tree fractal in C#

Posted on April 27, 2018 by RodStephens

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#

Posted on April 25, 2018 by RodStephens

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#

Posted on December 5, 2017 by RodStephens

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 | Leave a comment

Calculate Fibonacci words in C#

Posted on November 30, 2017 by RodStephens

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#

Posted on September 11, 2017 by RodStephens

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, non-differentiable function, Weierstrass curve, Weierstrass function, Windows Forms programming | Leave a comment

Draw a recursive overlapping snowflake fractal in C#

Posted on February 25, 2016 by Rod Stephens

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 →

Posted in fractals, graphics | Tagged C#, C# programming, example, example program, fractals, generator, graphics, initiator, overlapping snowflake fractal, recursion, snowflake, snowflake curve, snowflake fractal, Windows Forms programming | Leave a comment

Draw a recursive von Koch snowflake fractal in C#

Posted on February 25, 2016 by Rod Stephens

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 | Leave a comment

Draw a recursive snowflake fractal in C#

Posted on February 25, 2016 by Rod Stephens

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#

Posted on February 20, 2016 by RodStephens

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 | Leave a comment

Draw a curly tree fractal in C#

Posted on February 19, 2016 by RodStephens

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 →