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Quadratic koch island generator

World's simplest math tool

Free online quadratic Koch fractal generator. Just press a button and you'll get a quadratic Koch curve. There are no ads, popups or nonsense, just an awesome Koch island generator. Press a button – get a quadratic Koch flake. Created by mathematicians for mathematicians.
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Koch Flake Size and Iterations
Koch Flake width.
Koch Flake height.
How many times to apply transformation to every side of the starting square?
Koch Flake Colors
Background color of the Koch flake.
Color of Koch flake sides.
Fill color of the Koch flake.
Koch Flake Border Width and Padding
Thickness of the flake line.
Space between the flake and the edge of the image.
Quadratic koch island generator tool What is a quadratic koch island generator?
This tool draws quadratic Koch islands. The quadratic Koch island, also known as the quadratic Koch snowflake, is one of the varieties of the Koch curve. The base of the quadratic Koch flake is a square. At every iteration each side of the square is twisted into a new snake-like form. The rule for the side transformation is as follows – turn 90 degrees to the left, go up, turn 90 degrees to the right, go down, turn left, go right, turn right and go up. Becase the basis for this fractal is a closed square, the island after any number of iterations will stay closed, continuous and without self-intersections. You can control the number of iterations and increase or decrease the size of the fractal. You can select three colors for coloring the image. First for the background, second for the square sides, and third for the fill inside the closed figure. If you set the thickness of square side to 0, or remove it, only two colors will be used – for background and fill. You can also adjust distance from the edge of drawing area. Mathabulous!
Quadratic koch island generator examples Click to use
Generate a Third Order Quadratic Koch Curve
This example draws a quadric Koch flake using three iterations. Here two shades of blue are used for the background and fill, and white color for the contour. Canvas is 400x400px and line width is 4px.
Required options
These options will be used automatically if you select this example.
Koch Flake width.
Koch Flake height.
How many times to apply transformation to every side of the starting square?
Background color of the Koch flake.
Color of Koch flake sides.
Fill color of the Koch flake.
Thickness of the flake line.
Space between the flake and the edge of the image.
Generate a Vertically Oriented Quadratic Koch Island
This example is shaped vertically because the fractal height is larger than the width. We use 4 recrusive iterations for the island and sets the thickness of the quadratic flake line to 3 pixels.
Required options
These options will be used automatically if you select this example.
Koch Flake width.
Koch Flake height.
How many times to apply transformation to every side of the starting square?
Background color of the Koch flake.
Color of Koch flake sides.
Fill color of the Koch flake.
Thickness of the flake line.
Space between the flake and the edge of the image.
Draw a Detailed Quadratic Koch Flake in Two Colors
In this example we generate a more detailed 5th order quadric Koch flake. We also set the line thickness to zero and as a result the fractal generator uses only two colors – one for background and one for flake filling. We also set padding to 0 so the flake line touches the sides of the drawing area.
Required options
These options will be used automatically if you select this example.
Koch Flake width.
Koch Flake height.
How many times to apply transformation to every side of the starting square?
Background color of the Koch flake.
Color of Koch flake sides.
Fill color of the Koch flake.
Thickness of the flake line.
Space between the flake and the edge of the image.
Pro tips Master online math tools
You can pass options to this tool using their codes as query arguments and it will automatically compute output. To get the code of an option, just hover over its icon. Here's how to type it in your browser's address bar. Click to try!
https://onlinemathtools.com/generate-quadratic-koch-island?&width=400&height=400&iterations=3&background-color=%231904ff&line-segment-color=white&fill-color=%23020969&line-width=4&padding=10
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