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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Compute this fractal matrix
The unique-disjointness matrix ( UDISJ(n) ) is a matrix on all pairs of subsets of {1...,n} with entries $$ U_{(A,B)}=\begin{cases}
0, ~ if ~ |A\cap B|=1\\
1, ~ ...
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Create a triangle whose colors are determined by the bitsums of coordinates
Write a program that, for any \$n\$, generates a triangle made of hexagons as shown, \$2^n\$ to a side. The colors are to be determined as follows.
We may give the triangle barycentric coordinates so ...
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Fibonacci word fractal
The Fibonacci word is a sequence of binary strings defined as:
\$F_0 = \$ 0
\$F_1 = \$ 01
\$F_n = F_{n-1} F_{n-2}\$
The first ...
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Draw this fractal generated by applying Newton's method to cosh(x) - 1
I came across this picture the other day: (Credit to Josep M Batlle I Ferrer)
Your job is to generate this picture. This graph is generated by repeatedly applying newton's method to the graph of:
$$f(...
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Quicksand (piles)
In this fastest-code challenge, you take a positive integer as input, which represents the height of a sand pile, located at (0,0) on an infinite square grid. For example, if our input is ...
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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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Unicode T-square
Challenge
Create a function or program that, when given an integer size, behaves the following way:
If size is equal to 1, ...
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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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The Cantor Function
The Cantor function is continuous everywhere and constant almost everywhere, but has an average slope of 1:
The function can be found recursively:
\$f_0(x)=x\$
\$f_{n+1}(x)=\left\{\begin{matrix}\frac{...
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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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ASCII art H trees
An H tree is a fractal tree structure that starts with a line. In each iteration, T branches are added to all endpoints. In this challenge, you have to create an ASCII representation of every second H ...
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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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Generalized Cantor set segment lengths
Problem
Let's define a generalized Cantor set by iteratively deleting some rational length segments from the middle of all intervals that haven't yet been deleted, starting from a single continuous ...
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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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