{ "cells": [ { "cell_type": "markdown", "metadata": { "editable": true, "slideshow": { "slide_type": "" }, "tags": [] }, "source": [ "# 6. Fractals\n", "\n", "Walks does offer an internal structure unless we force them to pass through predefined points with fitted kernels. Fractals are mathematical sets that exhibit a repeating pattern at every scale. They have not only captivated mathematicians and scientists, but have also found a fascinating application in the world of music. The concept of fractals in music revolves around the idea of using these self-similar patterns to create compositions that can vary in complexity, embodying both a sense of infinity and a coherent structure. This approach to music composition allows for the exploration of new textures, forms, and sonic landscapes, pushing the boundaries of traditional musical creativity. Fractals inspired modern composers Jessie Montgomery in [Rounds for Piano and Orchestra](https://www.youtube.com/watch?v=eMYG_w6ueUg) and Dinuk Wijeratne in [Invisible cities](https://www.youtube.com/watch?v=sAK8aqAdUCA&t=1424s). Djalgo has four types of fractals: **cellular automata** (self-organizing systems governed by simple rules in a discrete grid), **Mandelbrot** (complex and infinitely detailed fractal structure), and **logistic map** (a simple mathematical model illustrating chaos theory)." ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "## Cellular automata\n", "\n", "Genius composer Iannis Xenakis might have been the first to popularize (or even to use) cellular automata in music with his orchestral work [Horos](https://www.youtube.com/watch?v=9aYsh8SRB-c) in 1986 ([Solomos, 2013](https://hal.science/hal-00770141)). This section applies a rather simple method to compose music with cellular automata, and can be summarized in three steps.\n", "\n", "1. Select a rule (among the 256 presented in the [Wolfram atlas](http://atlas.wolfram.com/01/01/)) and the initial state, then draw the cells.\n", "2. Select a strip along the sequence dimension.\n", "3. Apply notes and durations to transform the strip to a [digital piano roll](https://en.wikipedia.org/wiki/Piano_roll#In_digital_audio_workstations).\n", "\n", "These steps are shown in this 1 minute 13 seconds video. The music played in this video is the one we will compose here.\n", "\n", "
\n", "\n", "You can create an interesting score by hand, but inductively trying all sorts of scores, or complexifying the process by hand can be labourious. This is where Djalgo can help." ] }, { "cell_type": "code", "execution_count": 1, "metadata": { "editable": true, "metadata": {}, "slideshow": { "slide_type": "" }, "tags": [] }, "outputs": [], "source": [ "import djalgo as dj\n", "import numpy as np" ] }, { "cell_type": "markdown", "metadata": {}, "source": [ "We can start by plotting few cellular automata rules with a single cell initiating the pattern at the center of the first sequence." ] }, { "cell_type": "code", "execution_count": 2, "metadata": { "metadata": {} }, "outputs": [ { "data": { "image/png": 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