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Category Archives: fractals
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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Draw a colored Pickover popcorn fractal in C#
The example Draw a Pickover popcorn fractal in C# explains how to draw the basic Pickover popcorn fractal by iterating these equations: Xn+1 = Xn – h * Sin(Yn + Tan(3 * Yn)) Yn+1 = Yn – h * Sin(Xn … Continue reading
Draw a Pickover popcorn fractal in C#
This program maps an iterated function system in its drawing area onto the region 4 <= x <= 4, 3 <= y <= 3. If you click on a point, the program iterates these equations and plots the points: Xn+1 … Continue reading
Posted in algorithms, drawing, fractals, graphics, mathematics
Tagged algorithms, C#, C# programming, drawing, example, example program, fractals, graphics, mathematics, Pickover, Pickover fractal, popcorn fractal, Windows Forms programming
3 Comments
Draw four interlocking Heighway dragons in C#
One of the interesting features of the Heighway dragon curve is that it can interlock with itself as shown in this picture. The four curves all start at the same point in the middle of the picture and each is … Continue reading
Posted in algorithms, drawing, fractals, graphics, mathematics
Tagged algorithms, C#, C# programming, center Heighway curve, center Heighway dragon, drawing, example, example program, fractals, graphics, Heighway curve, Heighway dragon, interlocking Heighway curve, interlocking Heighway dragon, mathematics, Windows Forms programming
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Center a Heighway dragon fractal in C#
The example Draw a Heighway dragon fractal in C# explains how to draw a Heighway dragon. That example draws its curve somewhere near the center of the form but the curve isn’t really centered. To properly size and center the … Continue reading
Draw a Heighway dragon fractal in C#
The Heighway dragon, which is also known as the Harterâ€“Heighway dragon, is a recursive curve where each level of recursion provides more detail. The base case where the level of recursion is 0 is a straight line. From any given … Continue reading
Posted in algorithms, drawing, fractals, graphics, mathematics
Tagged algorithms, C#, C# programming, drawing, example, example program, fractals, graphics, Heighway curve, Heighway dragon, mathematics, Windows Forms programming
1 Comment
Use a queue to draw a breadthfirst colored binary tree in C#
The example Draw a breadthfirst colored binary tree in C# shows how to use a Stack to draw a binary tree in depthfirst order. The program builds a Stack representing the bottom (trunk) level of the tree. For each level, … Continue reading
Posted in algorithms, drawing, fractals, graphics
Tagged algorithms, binary tree, breadthfirst, breadthfirst tree, C#, C# programming, color, drawing, example, example program, fractal, graphics, queue, recursion, Stack, tree, Windows Forms programming
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Draw a breadthfirst colored binary tree in C#
The example Draw a colored binary tree in C# shows how to use recursion to draw a colored binary tree. If you look closely at a tree of high degree, however, you’ll notice a problem. The program draws a branch … Continue reading
Posted in algorithms, drawing, fractals, graphics
Tagged algorithms, binary tree, breadthfirst, breadthfirst tree, C#, C# programming, color, drawing, example, example program, fractal, graphics, recursion, tree, Windows Forms programming
4 Comments