Questions tagged [fractal]
Fractals are shapes that are self-similar and are usually quite detailed. Well-known fractal sets include the Mandelbrot set, Julia sets, and Phoenix sets. Tree-like fractal drawings are also common.
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Draw a Fibonacci Swoosh
Title courtesy of Greg Martin
For this challenge, I'll define an arc of size \$k\$ as a single piece of a sine wave with a length of \$k\$ units and an height of \$\frac{k}{4}\$ units:
And I'll ...
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Create a triangle whose colors are determined by the bitsums of coordinates
Write a program that, for any \$n\$, generates a triangle made of hexagons as shown, \$2^n\$ to a side. The colors are to be determined as follows.
We may give the triangle barycentric coordinates so ...
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Draw this fractal generated by applying Newton's method to cosh(x) - 1
I came across this picture the other day: (Credit to Josep M Batlle I Ferrer)
Your job is to generate this picture. This graph is generated by repeatedly applying newton's method to the graph of:
$$f(...
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Double the diagonal squares
Given a positive integer N, output this doubling pattern of slash squares/rectangles.
For N=1, the base is:
...
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Eye test - How many squares are in this picture?
The picture:
Sick of the same old grid where the answer is simply a square pyramidal number?
Accept the challenge and write a program that given a positive integer \$n\$ counts how many squares are in ...
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Hilbertize an image
For a computer vision app I want to do a mapping of an image, in such a way that every pixel fit hilbert curve, instead of conventional layout. So task could be as follows:
Task description
Given ...
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Drawing the Peano curve
Introduction
In geometry, the Peano curve is the first example of a space-filling curve to be discovered, by Giuseppe Peano in 1890. Peano's curve is a surjective, continuous function from the unit ...
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Create an "H" from smaller "H"s
Challenge
Create a function or program that, when given an integer size, does the following:
If size is equal to 1, output
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Generate TeX to typeset Sierpinski Triangle Fractal
Challenge
Write code that outputs TeX (LaTeX) math-equation code (given below) that will typeset Sierpinski Triangle Fractal of 5 levels. Shortest code wins.
Details
TeX (and friends like LaTeX, ...
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The strange attraction of the logistic map
The purpose of the challenge is to approximately plot the attractor of the logistic map as a function of its parameter r (also called bifurcation diagram), or a subregion of it. The appearance of the ...
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Make Some Snow!
Your task: generate a Koch snowflake to the nth depth. You do not need to make a complete Koch snowflake, just one side of the starting triangle. Wikipedia on Koch flakes: https://en.wikipedia.org/...
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Is it within the Cantor set?
The Challenge
For this challenge, you are supposed to determine if a given number is in the Cantor set. So first, let's define the Cantor set.
First, start with the numbers between 0 and 1. Any ...
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Generate a Padovan Spiral
Introduction
Similar to the Fibonacci Sequence, the Padovan Sequence (OEIS A000931) is a sequence of numbers that is produced by adding previous terms in the sequence. The initial values are defined ...
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ASCII Hilbert Curve
Given an integer n output the nth iteration of the Hilbert Curve in ASCII using the characters ...
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Draw a Dragon Curve
You task for today: draw a dragon curve!
In case you don't know what a Dragon Curve is, here is an introductory ViHart video (Really cool, please watch!)
Your task: draw a dragon curve, iterated at ...
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Draw the Hilbert Curve
A Hilbert Curve is a type of space-filling curve, and it basically maps a line to a plane. Each point in the line corresponds to just one point in the plane, and each point in the plane corresponds to ...
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Computer Generated Cracked Soil
Write a program that takes in an integer from 0 to 65535 (216-1) and generates a unique 500×500 pixel image that looks as similar as possible to these 6 real life images of cracked soil:
These ...
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Gasket Weaving - draw a Sierpiński knot
Given an integer N >= 2, produce an image showing a Sierpiński knot of degree N.
For example, here are knots of degree 2, 3, 4 and 5:
Click on the images to view full size (the higher the degree the ...
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Map string to Hilbert curve
Let's map some strings to 2d space, fractal style. Your task is to compute a Hilbert curve and lay a string along it.
Task
The task is to take the single-line input string, and lay it out along a ...
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Converging Sums of a Fractal Sequence
Background
A fractal sequence is an integer sequences where you can remove the first occurrence of every integer and end up with the same sequence as before.
A very simple such sequence is called ...
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Beta's Snowflake
Challenge
Winter is fast approaching with many places receiving the first layers of snow for the 15/16 season, so why don't we break out the snow machines and code ourselves some snow?
Given a ...
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ASCII Dragon's Curve
Introduction
The Dragon's Curve is a fractal curve that notably appears on section title pages of the Jurassic Park novel.
It can very simply be described as a process of folding a paper strip, as ...
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ASCII art square affine fractals
Write the smallest program you can to create affine fractals. You may use any method you feel like that generates the same results as the rules below. You don't have to use any ideas from the ...
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Word fractal plotter
Iterated Function Systems
An Iterated Function System (IFS) is a method of constructing self-similar fractals. Each fractal is defined recursively as the union of several copies of itself, with each ...
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Draw a Random Walk with Slashes
Write a program or function that takes in a positive integer N (via stdin/command line/function arg) and prints or returns a string representation of a two dimensional random walk that is N steps long,...
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