GPU Fractal Explorer

A real-time, GPU-accelerated fractal visualizer with Max/MSP integration (via jweb), OSC control, and sonification analysis output for live performance and parameter automation.

Features

• 6 Fractal Types: Mandelbrot, Burning Ship, Multibrot, Newton, Clifford Attractor, Domain Coloring
• GPU Accelerated: Real-time rendering via WebGL2 fragment shaders
• Max/MSP Integration: Load in jweb and control via Max messages
• OSC Control: Bidirectional WebSocket bridge for external OSC control
• Sonification Analysis: 13 toggleable analysis channels for audio-reactive applications
• Animation: Auto-zoom, color cycling, parameter animation
• 7 Color Schemes: Classic, Fire, Ocean, Rainbow, Grayscale, Psychedelic, Electric
• Touch Support: Pinch-to-zoom and drag on mobile/tablet

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Quick Start

Option 1: Standalone Browser

Simply open fractals-max.html in Chrome, Firefox, or Edge.

Option 2: Max/MSP (jweb)

[jweb @url fractals-max.html]

Then send messages to the jweb object (see Command Reference below).

Option 3: With OSC Control + Analysis Output

# Start the WebSocket bridge
node osc-bridge.js 9000 8080 9001

# Bridge configuration:
#   UDP 9000 - OSC input (control messages)
#   WS  8080 - WebSocket (browser connection)
#   UDP 9001 - OSC output (analysis data)

Then click "Connect" in the HTML interface.

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Sonification Analysis System

The visualizer includes a comprehensive analysis system that extracts musical/sonic parameters from the fractal visualization in real-time. Each channel can be independently toggled on/off.

Analysis Channels

Channel	Output	Description
brightness	float 0-1	Average luminance of viewport
escapeRatio	float 0-1	Density of escaped pixels (vs. in-set)
edgeDensity	float 0-1	Amount of boundary/edge detail
dominantHue	float 0-1	Hue of average color
colorBalance	3 floats	RGB balance (r, g, b)
spectralCentroid	2 floats	Brightness-weighted center (x, y)
grid	N² floats	Spatial brightness grid (4×4 to 16×16)
columnSums	128 floats	Vertical projection (spectrogram-like)
rowSums	128 floats	Horizontal projection (waveform-like)
ring	N floats	Radial samples around center (8-64)
iterHist	16 floats	Iteration count histogram
zoomParams	multiple	Normalized zoom, position data
fractalParams	multiple	Current fractal type, Julia C, etc.

Sonification Mapping Ideas

Analysis Channel	Musical Parameter
brightness	Filter cutoff, amplitude
escapeRatio	Texture density, grain rate
edgeDensity	Harmonic content, distortion
dominantHue	Pitch, timbre morph
colorBalance	Stereo position, 3-band EQ
spectralCentroid	Spatial panning
grid	Wavetable, FM matrix
columnSums	Additive synthesis spectrum
rowSums	Amplitude envelope
ring	Arpeggio sequence
iterHist	Spectral shape

Analysis Configuration

Command	Args	Description
anrate	1-60	Analysis rate in fps
angridsize	2-32	Grid resolution (N×N)
anringsamples	4-128	Ring sample count

Channel Toggle Commands

Each channel has on/off commands via Max messages or OSC:

an_brightness 1      Enable brightness output
an_brightness 0      Disable brightness output
an_escape 1          Enable escape ratio
an_edge 1            Enable edge density
an_hue 1             Enable dominant hue
an_color 1           Enable color balance
an_centroid 1        Enable spectral centroid
an_grid 1            Enable spatial grid
an_columns 1         Enable column sums
an_rows 1            Enable row sums
an_ring 1            Enable ring samples
an_hist 1            Enable iteration histogram
an_zoom 1            Enable zoom/position params
an_params 1          Enable fractal params

Bulk Commands

Command	Description
an_all_on	Enable all analysis channels
an_all_off	Disable all analysis channels
an_basic_on	Enable brightness, escape, edge
an_spatial_on	Enable grid, columns, rows, ring

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Analysis Output (OSC)

When using the OSC bridge, analysis data is sent to the output port (default 9001):

/fractal/analysis/brightness 0.342
/fractal/analysis/escapeRatio 0.723
/fractal/analysis/edgeDensity 0.156
/fractal/analysis/dominantHue 0.65
/fractal/analysis/colorBalance 0.4 0.3 0.5
/fractal/analysis/spectralCentroid 0.52 0.48
/fractal/analysis/grid 0.1 0.2 0.3 ... (N² values)
/fractal/analysis/columnSums 0.1 0.2 ... (128 values)
/fractal/analysis/rowSums 0.1 0.2 ... (128 values)
/fractal/analysis/ring 0.3 0.5 0.2 ... (N values)
/fractal/analysis/iterHist 0.1 0.05 0.2 ... (16 values)
/fractal/analysis/zoom 0.28
/fractal/analysis/position 0.45 0.52

Max/MSP Analysis Output

When running in jweb, analysis data comes out the outlet:

[jweb]
   |
[route analysis]
   |
[route brightness escapeRatio edgeDensity ...]

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Command Reference

All commands work via Max messages (to jweb) and OSC (via WebSocket bridge).

Fractal Type Selection

Command	Args	Description
type	0-5	Set fractal by number
mandelbrot	-	Type 0: Classic Mandelbrot set
burningship	-	Type 1: Burning Ship fractal
multibrot	-	Type 2: Generalized z^d + c
newton	-	Type 3: Newton root-finding fractal
clifford	-	Type 4: Clifford strange attractor
domain	-	Type 5: Complex function visualization

Navigation

Command	Args	Range	Description
centerX / cx	float	-2 to 2	Center X coordinate
centerY / cy	float	-2 to 2	Center Y coordinate
center	x y		Set both coordinates
zoom	float	-2 to 45	Zoom level (log₂ scale)
reset	-		Reset to default view

Rendering

Command	Args	Range	Description
maxIter	int	50-5000	Maximum iterations
iter	int	50-5000	Alias for maxIter

Colors

Command	Args	Range	Description
colorScheme / scheme	int	0-6	Color palette number
colorOffset / offset	float	0-1	Color phase offset
colorFreq / freq	float	0.1-10	Color frequency

Color Scheme Shortcuts: classic, fire, ocean, rainbow, grayscale, psychedelic, electric

Julia Mode (Mandelbrot / Burning Ship / Multibrot)

Command	Args	Description
juliaMode	0/1	Toggle Julia mode
julia	x y	Set Julia C constant (enables Julia)
juliaX / jx	float	Julia C real part (-2 to 2)
juliaY / jy	float	Julia C imaginary part (-2 to 2)
julia_on / julia_off	-	Enable/disable Julia mode

Multibrot Parameters

Command	Args	Range	Description
power	float	2-8	Exponent d in z^d + c

Newton Fractal Parameters

Command	Args	Range	Description
newtonPoly / poly	int	0-3	Polynomial selection (z³-z⁶)
newtonRelax / relax	float	0.1-2	Relaxation factor

Clifford Attractor Parameters

Command	Args	Range	Description
cliffordA / ca	float	-3 to 3	Parameter a
cliffordB / cb	float	-3 to 3	Parameter b
cliffordC / cc	float	-3 to 3	Parameter c
cliffordD / cd	float	-3 to 3	Parameter d
cliff	a b c d		Set all four parameters

Domain Coloring Parameters

Command	Args	Range	Description
domainFunc / func	int	0-9	Complex function
domainGrid / grid	0/1		Toggle grid lines

Animation

Command	Args	Description
autoZoom / autozoom	0/1	Toggle auto-zoom
colorCycle / cycle	0/1	Toggle color cycling
animateParams / animate	0/1	Toggle parameter animation
animSpeed / speed	float	Animation speed (0.1-3)

UI Control

Command	Description
hideui	Hide control panel
showui	Show control panel
toggleui	Toggle control panel

State

Command	Description
getstate / dump	Output full state as JSON
getanalysis / dumpanalysis	Output analysis config as JSON

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Max/MSP Examples

Basic Setup with Analysis

[jweb @url fractals-max.html @size 800 600]
   |
[route analysis state]
   |           |
[route brightness escapeRatio edgeDensity]
   |           |              |
[number]   [number]       [number]

Audio-Reactive Sonification

[adc~]
   |
[peakamp~ 100]
   |
[scale 0. 1. 0. 1.]
   |
[prepend offset]
   |
[jweb]
   |
[route analysis]
   |
[route brightness]
   |
[scale 0. 1. 200. 2000.]
   |
[line~]
   |
[lores~ 1000 0.5]

Using Analysis Grid for Synthesis

[jweb]
   |
[route analysis]
   |
[route grid]
   |
[zl.stream 64]  // 8x8 grid = 64 values
   |
[jit.fill jit_matrix 8 8]
   |
[jit.matrix 1 float32 8 8]

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SuperCollider Example with Analysis

// Receive analysis from bridge
OSCdef(\fractalBrightness, { |msg|
    ~brightness = msg[1];
    ~synth.set(\cutoff, msg[1].linexp(0, 1, 200, 8000));
}, '/fractal/analysis/brightness');

OSCdef(\fractalEdge, { |msg|
    ~edgeDensity = msg[1];
    ~synth.set(\distortion, msg[1]);
}, '/fractal/analysis/edgeDensity');

// Send control
n = NetAddr("localhost", 9000);
n.sendMsg('/fractal/type', 0);
n.sendMsg('/fractal/an_basic_on');

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Keyboard Shortcuts (in browser)

Key	Action
H	Toggle UI panel
R	Reset view
J	Toggle Julia mode
Space	Toggle auto-zoom
C	Toggle color cycling
1-6	Select fractal type
+ / -	Zoom in/out
Arrows	Pan view

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Mouse/Touch Controls

Action	Description
Drag	Pan view
Scroll / Pinch	Zoom in/out
Double-click	Center on point
Shift+Double-click	Pick Julia C from Mandelbrot

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Performance Tips

1. Lower analysis rate (anrate 15) for complex patches
2. Disable unused channels to reduce CPU overhead
3. Lower iterations for smoother animation at deep zooms
4. Clifford attractor recomputes on parameter change (may stutter during animation)
5. Chrome/Edge typically have best WebGL2 performance

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License

MIT

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Credits

Created for live audio-visual performance with Max/MSP, SuperCollider, and TouchOSC.