FRACTALS IN MUSIC - Exploration & Experiment
TLDRThe video script narrates the innovative use of fractals in computer graphics and music. In 1978, Lauren Carpenter used fractals to create computer-generated images of mountains for Boeing's advertisements, a task previously deemed impossible due to computational limitations. This groundbreaking work laid the foundation for CGI in films, such as Star Trek II: The Wrath of Khan. The script then explores the concept of fractals, which are self-replicating patterns found in nature and various scientific fields. The creator experiments with fractals in music by layering a melody at different speeds and pitches to harmonize, and introduces an auditory illusion to create a sense of indefinite acceleration or deceleration in rhythm. The video concludes with the idea of fractal music, where a piece is composed of the same music played at various speeds, creating a complex, layered auditory experience.
Takeaways
- 🚀 **Fractals in Computer Graphics**: In 1978, Lauren Carpenter used fractals to generate computer images of mountains for Boeing's advertisements, which was a groundbreaking application of fractals in computer graphics.
- 📚 **Mandelbrot's Influence**: Benoit Mandelbrot's work on fractals, particularly his book 'Fractals: Form, Chance and Dimension', was instrumental in enabling Carpenter to use fractals for computer-generated imagery.
- 🏔️ **Fractal Visualization**: Fractals allowed for the creation of complex shapes like mountains from simple geometric forms by iteratively splitting shapes into smaller parts.
- 🎬 **CGI in Film**: Carpenter's work with fractals at Lucasfilm led to the first fully computer-generated scene in a full-length movie, 'Star Trek II: The Wrath of Khan'.
- 🎶 **Fractals in Music**: The concept of fractals can be applied to music by creating melodies that repeat at different scales and speeds, creating harmonies with themselves.
- 🎼 **Consonance in Fractal Music**: To ensure harmony, the script suggests using notes from a minor 9th chord to create a melody that is consonant across different layers and speeds.
- 🔄 **Iterative Melody Transformation**: The melody can be transformed iteratively by changing pitch, speed, tone, and other parameters to create a fractal-like pattern in music.
- 🎧 **Auditory Illusions**: The Shepherd's Tone, an auditory illusion, can be used to create the sensation of a melody or rhythm accelerating indefinitely.
- 🔁 **Seamless Loops**: By duplicating tracks and adjusting pitch and fade, a seamless loop can be created, giving the impression of a melody that could continue infinitely.
- 🎵 **Multilayered Fractal Music**: The entire piece of music can be constructed using fractal principles, with each note or rhythm containing the essence of the same fractal pattern.
- 🌐 **Endless Possibilities**: The depth of fractal music can be explored further by increasing the number of iterations, offering a vast potential for creativity and experimentation.
Q & A
What was the challenge Lauren Carpenter faced when he wanted to include a mountain in the background of Boeing's aircraft images?
-The challenge was that in 1978, computers did not have the power to handle the millions of polygons needed to model a mountain, and there was no existing software to do that.
How did fractals help in generating computer images of mountains for Boeing's aircraft?
-Fractals, as theorized by Benoit Mandelbrot, allowed Carpenter to create mountains using a few triangles, which the computer could then iteratively split into smaller ones, creating more and more detail with each iteration.
What significant contribution did Lauren Carpenter make to the field of computer-generated imagery (CGI)?
-Carpenter's use of fractals to generate images led to the first scene entirely in CGI in a full-length cinema movie, which was for the movie 'Star Trek II: The Wrath of Khan'.
How are fractals used to create never-ending patterns that repeat themselves indefinitely at different scales?
-Fractals are mathematical shapes that can be infinitely zoomed in on, and at each level of magnification, the general shape of the fractal can be found within itself, creating a self-similar pattern.
What is the concept of using fractals to create music, as discussed in the script?
-The concept involves creating a melody and layering it with the same melody played at different speeds, resulting in the same pattern repeated at different scales, akin to the self-similarity in fractals.
How did the creator approach the challenge of ensuring consonance among notes when layering melodies at different speeds?
-The creator decided to work with the notes of a minor 9th chord (A minor 9), which when played together form a consonant chord, allowing for harmonization at different speeds without dissonance.
What was the approach to modifying the melody to improve its harmonization at different speeds?
-The creator started with a basic melody using the notes of the A minor 9 chord, copied it into different tracks to play at different speeds, and then made adjustments to the melody where needed through a process of trial and error.
How does the iterative logic of fractals apply to modifying the tone or timbre of a sound in music?
-The iterative logic can be applied by starting with a simple sound and then applying transformations to it, such as changing the note length, reverb width, or distortion level, with each iteration as the melody gets faster.
What auditory illusion is used to create the sensation of a note or rhythm going up or down in pitch indefinitely?
-The Shepherd's Tone illusion is used, which is created by three parallel notes with an interval of an octave between each, all slowly increasing in pitch to create a continuous ascending or descending effect.
How can the concept of zooming in on fractals indefinitely to find new details be applied to music?
-The concept can be applied by creating a loop in music that accelerates indefinitely, giving the feel of a zoom in or zoom out, using auditory illusions like the Shepherd's Tone to maintain a seamless and continuous progression.
What is the final concept proposed for creating a fractal music piece that evolves progressively?
-The final concept involves introducing the basic melody first, then adding other layers at different speeds, and finally accelerating the music to create a piece that evolves and deepens with each iteration, reflecting the self-similarity and iterative nature of fractals.
Outlines
🚀 The Birth of Fractal Imagery in CGI
In 1978, Boeing was designing experimental aircraft with unusual shapes. To visualize these designs, computer scientist Lauren Carpenter used fractals, a mathematical concept by Benoit Mandelbrot, to generate images of mountains for the aircraft's backdrop. Fractals, which create self-similar patterns at different scales, revolutionized computer graphics. Carpenter's work led to the first full CGI scene in a movie, 'Star Trek II: The Wrath of Khan'. Fractals are also found in nature and have applications in fields like economics and telephony.
🎼 Creating Fractal Music Through Melody and Harmony
The speaker explores the application of fractals to music by creating a melody and layering it at different speeds to achieve a harmonizing effect at various tempos. Using a minor 9th chord, the melody is manipulated across multiple tracks to ensure consonance. The process involves iterative adjustments to refine the harmonization. The concept of fractal iteration is then applied to the tone and timbre of the sound, with transformations such as increasing speed, shortening notes, widening reverb, and adding distortion as the melody progresses.
🌀 Infinite Zoom and the Shepherd's Tone Illusion
The speaker discusses the possibility of creating a fractal-like experience in music by using the auditory illusion similar to a Shepherd's Tone, which gives the sensation of indefinite pitch change. By layering three rhythms at different speeds and gradually increasing their tempo, an illusion of perpetual acceleration is achieved. The challenge of different octaves is addressed by duplicating tracks and adjusting their pitch to create a seamless loop. The concept is further extended by speeding up the entire song to a continuous note and using it to play the same music, creating a fractal music structure where each note contains the same fractal music within it.
Mindmap
Keywords
💡Fractals
💡Benoit Mandelbrot
💡Lauren Carpenter
💡Computer-Generated Imagery (CGI)
💡Minor 9th Chord
💡Iterative Logic
💡Shepherd's Tone
💡Pentatonic Scale
💡Consonance
💡Psychedelic Movement
💡Economic and Telephony Applications
Highlights
In 1978, Boeing was designing experimental aircraft with unusual shapes, which were visualized with the help of computer-generated images by Lauren Carpenter.
Lauren Carpenter wanted to include a mountain in the background of the aircraft images, inspired by Boeing's advertisements.
The computational power of computers in 1978 was insufficient to model a mountain with millions of polygons.
There was no existing software to generate mountains, making the task initially impossible for Carpenter.
Carpenter discovered fractals and the work of Benoit Mandelbrot, which revolutionized how mountains could be generated by computers.
Fractals enabled the creation of complex shapes like mountains from simple starting points through iterative processes.
Carpenter's work led to the first fully computer-generated scene in a cinema movie, 'Star Trek II: The Wrath of Khan'.
Fractals are mathematical patterns that repeat indefinitely at different scales, found in nature and various scientific fields.
The concept of fractals was used to create a unique musical piece by layering melodies at different speeds and octaves.
A minor 9th chord was used to ensure consonance between different notes played simultaneously.
Melodies with rhythmic variations did not harmonize well, leading to a preference for a steady pulse.
Iterative logic similar to fractals was applied to musical parameters such as tone, timbre, and reverb to create a unique auditory experience.
The Shepherd's Tone auditory illusion was adapted to create a sense of indefinite rhythmic acceleration.
A loop was created to give the illusion of indefinite acceleration by blending melodies played at different speeds and octaves.
The concept of fractal music involves each note being composed of the same fractal music, creating a self-similar pattern at different scales.
The video explores the idea of creating a fractal music piece by progressively introducing layers and accelerating the melody.
The final track combines the various stages of fractal music creation, showcasing how the piece evolves over time.
Transcripts
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