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<!DOCTYPE html>
<html lang="en">
<head>
<title>Refractal</title>
<link href="style.css" rel="stylesheet">
<script src="lib/webgl-utils.js"></script>
<script src="lib/webgl-debug.js"></script>
<script src="lib/cuon-utils.js"></script>
<script src="js/util.js"></script>
<script src="js/escape-time.js"></script>
<script src="js/lyapunov.js"></script>
<script src="js/root-finding.js"></script>
<script src="js/pendulum.js"></script>
<script src="js/recursive.js"></script>
<script src="js/main.js"></script>
</head>
<body onload="main()">
<div class="main">
<canvas id="fractal_canvas" width=1000px height=1000px></canvas>
<canvas id="path_canvas" width=1000px height=1000px></canvas>
<div class="sidebar">
<details open=true>
<summary>
Program
</summary>
<select id="program">
<option value="escape-time">Escape Time</option>
<option value="lyapunov">Lyapunov</option>
<option value="root-finding">Root Finding</option>
<option value="recursive">Recursive</option>
<option value="pendulum">Pendulum</option>
</select>
</details>
<div id="escape_time_options">
<details open=true>
<summary>
Fractal options
</summary>
Fractal:
<select id="esc_fractal">
<optgroup label="Mandelbrot family">
<option value=0>Mandelbrot</option>
<option value=1>Burning Ship</option>
<option value=2>Tricorn/Mandelbar</option>
<option value=44>Perpendicular Mandelbrot</option>
<option value=45>Celtic Mandelbrot</option>
<option value=46>Celtic Mandelbar</option>
<option value=47>Perpendicular Celtic</option>
<option value=48>Heart Mandelbrot</option>
<option value=39>Perpendicular Burning Ship</option>
<option value=49>Buffalo</option>
<option value=50>Celtic Heart</option>
<option value=51>Perpendicular Buffalo</option>
<option value=5>Multibrot</option>
<option value=40>Multi-Burning Ship</option>
<option value=52>Multi-Mandelbar</option>
<option value=23>Complex Multibrot</option>
<option value=53>Complex Multi-Burning Ship</option>
<option value=54>Complex Multi-Mandelbar</option>
</optgroup>
<optgroup label="Uncommon Mandelbrot family">
<option value=58>Airship</option>
<option value=59>Tail</option>
<option value=60>Quill</option>
<option value=61>Shark Fin</option>
<option value=62>Power Drill</option>
<option value=63>Big and Little</option>
<option value=64>Halo</option>
<option value=65>Genie Lamp</option>
<option value=66>Hook</option>
<option value=67>Cow</option>
<option value=68>Sideways Ship</option>
<option value=69>Sock Puppet</option>
<option value=70>Speedy Buffalo</option>
<option value=71>Australia</option>
<option value=72>Smart Buffalo</option>
</optgroup>
<optgroup label="Mandelbrot variants">
<option value=26>Other Buffalo</option>
<option value=17>Simonbrot</option>
<option value=15>Rational Map</option>
<option value=16>Phoenix</option>
<option value=18>Tippetts</option>
<option value=25>Meta-Mandelbrot</option>
<option value=32>Zubieta</option>
<option value=33>Cubic</option>
<option value=36>Twin Mandelbrot</option>
<option value=41>Mandelbrot Foam</option>
<option value=55>Fraktal 1</option>
<option value=56>Fraktal 2</option>
</optgroup>
<optgroup label="Other Fractals">
<option value=3>Heart</option>
<option value=4>Mandelbox</option>
<option value=6>CodeParade's Feather</option>
<option value=22>CodeParade's SFX</option>
<option value=14>Sine</option>
<option value=19>Marek Dragon</option>
<option value=20>Gangopadhyay</option>
<option value=21>Exponent</option>
<option value=24>Thorn</option>
<option value=27>Magnet</option>
<option value=28>Triple Dragon</option>
<option value=29>Spiral</option>
<option value=31>Hyperbolic Sine</option>
<option value=42>Collatz 1</option>
<option value=43>Collatz 2</option>
<option value=57>Cactus</option>
</optgroup>
<optgroup label="Chaotic Maps">
<option value=7>Chirikov</option>
<option value=11>Modified Duffing</option>
<option value=12>"Gingerbread"</option>
<option value=13>Hénon</option>
<option value=34>Logistic</option>
</optgroup>
<optgroup label="Custom">
<option value=8>Smelly Shoe</option>
<option value=9>Dog Skull</option>
<option value=30>Mandelbruh</option>
<option value=35>Tricorn Sine</option>
<option value=37>Fracktail</option>
<option value=38>Sauron</option>
<option value=73>Custom</option>
</optgroup>
</select>
<hr>
z = x + yi
<div id="esc_function_text" style="font-family: monospace">
z ← z<sup>2</sup> + c
</div>
<div id="scaling_div" style="display: none" esc_param=1>
Scale:
<input id="scaling" type=number value=2.0 step=0.025>
</div>
<div id="exponent_div" style="display: none" esc_param=1>
p:
<input id="exponent" type=number value=2.0 step=0.025>
</div>
<div id="rational_div" style="display: none">
p:
<input id="rational_p" type=number value=2.0 step=0.025 min=0 esc_param=1>
<br>
q:
<input id="rational_q" type=number value=-2.0 step=0.025 max=0 esc_param=2>
<br>
λ:
<input id="rational_lambda" type=number value=0.0 step=0.0025 esc_param=3>
</div>
<div id="phoenix_div" style="display: none">
<div id="phoenix_p_text" class="complex-text">
p = 0 + 0i
</div>
<canvas id="phoenix_p_selector" class="selector" width=200px height=200px></canvas>
</div>
<div id="dragon_div" style="display: none">
r:
<input id="dragon_r" type=number value=0.041 step=0.001 esc_param=1>
</div>
<div id="gangopadhyay_div" style="display: none">
ax1:
<input id="gangopadhyay1" type=checkbox>
ax2:
<input id="gangopadhyay2" type=checkbox>
ax3:
<input id="gangopadhyay3" type=checkbox checked=true>
ax4:
<input id="gangopadhyay4" type=checkbox checked=true>
ax5:
<input id="gangopadhyay5" type=checkbox>
</div>
<div id="cmultibrot_div" style="display: none">
<div id="cmultibrot_p_text" class="complex-text">
p = 2 + 0i
</div>
<canvas id="cmultibrot_p_selector" class="selector" width=200px height=200px></canvas>
</div>
<div id="mandelbruh_div" style="display: none">
a:
<input id="mandelbruh_a" type=number value=2.0 step=0.1 esc_param=1>
</div>
<div id="hyperbolic_sine_div" style="display: none">
p:
<input id="hyperbolic_sine_p" type=number value=2.0 step=0.025 esc_param=1>
</div>
<div id="zubieta_div" style="display: none">
<div id="zubieta_a_text" class="complex-text">
a = 1 + 0i
</div>
<canvas id="zubieta_a_selector" class="selector" width=200px height=200px></canvas>
</div>
<div id="sauron_div" style="display: none">
<div id="sauron_a_text" class="complex-text">
a = 0 + 0i
</div>
<canvas id="sauron_a_selector" class="selector" width=200px height=200px></canvas>
</div>
<div id="foam_div" style="display: none">
<div id="foam_q_text" class="complex-text">
q = 0 + 0i
</div>
<canvas id="foam_q_selector" class="selector" width=200px height=200px></canvas>
</div>
</details>
<details id="julia_div">
<summary>
Julia Set view
</summary>
Max julification = normal julia set.
<br>
Julification:
<input id="julification" type=range min=0 max=1 value=0 step=0.01>
<div id="esc_julia_text" class="complex-text">
c = 0 + 0i
</div>
<canvas id="julia_selector" class="selector" width=200px height=200px></canvas>
</details>
<details open=true>
<summary>
Iteration parameters
</summary>
Escape Algorithm:
<select id="escape_algorithm">
<option value=0>Magnitude</option>
<option value=1>Derivative Bailout</option>
</select>
<div id="esc_mag_div">
Escape Magnitude:
<input id="escape_radius" type=number value=2 step=0.1 min=0>
</div>
<div id="esc_der_div" style="display: none">
Derivative Bailout Magnitude:
<input id="escape_derivative" type=number value=1000 step=25 min=0>
</div>
Max Iterations:
<input id="esc_max_iterations" type=number value=30 step=5 min=0>
</details>
<details>
<summary>
Orbit traps
</summary>
Enable orbit trap colouring to see.
<br>
<button id="orbit_trap_add">
Add new
</button>
<div id="orbit_traps" style="display: grid">
</div>
</details>
<details open=true>
<summary>
Exterior colouring
</summary>
<div>
Style:
<select id="exterior_colouring_style">
<option value=0>Monotonic</option>
<option value=1>Cyclic</option>
<option value=2>Radial</option>
</select>
</div>
<div id="monotonic_rendering_div">
Function:
<select id="monotonic_function">
<optgroup label="Escape Time">
<option value=0>Discrete</option>
<option value=1 selected>Smooth</option>
<option value=5>Derivative Smooth</option>
</optgroup>
<optgroup label="Other">
<option value=2>Normal Map</option>
<option value=3>Stripe Average</option>
<option value=4>Orbit Trap</option>
</optgroup>
</select>
<hr>
Easing Function:
<select id="monotonic_easing_function">
<optgroup label="Polynomial">
<option value=8>Quintic Root</option>
<option value=6>Quartic Root</option>
<option value=4>Cube Root</option>
<option value=2>Square Root</option>
<option value=0 selected>Linear</option>
<option value=1>Quadratic</option>
<option value=3>Cubic</option>
<option value=5>Quartic</option>
<option value=7>Quintic</option>
</optgroup>
<optgroup label="Other">
<option value=9>Exponential</option>
<option value=10>Sine</option>
</optgroup>
</select>
<br>
Ease Out:
<input type=checkbox id="monotonic_ease_out">
<div id="light_selector_div" style="display: none">
Light Position:
<br>
<canvas id="light_selector" class="selector" width=200px height=200px></canvas>
</div>
<div id="stripe_average_div" style="display: none">
Stripe Density:
<input id="stripe_density" type=number value=3 min=0 step=0.1>
</div>
</div>
<div id="cyclic_rendering_div" style="display: none">
Cycle Function:
<select id="cyclic_cycle_function">
<option value=0>Escape Time</option>
<option value=1>Orbit Exponential</option>
<option value=2>Orbit Trap</option>
</select>
<br>
Waveform:
<select id="cyclic_waveform">
<option value=0>Sine</option>
<option value=1>Square</option>
<option value=2>Triangle</option>
<option value=3>Sawtooth</option>
</select>
<br>
Period:
<input id="esc_cycle_period" type=number value=1 min=0 step=0.01>
</div>
<div id="radial_rendering_div" style="display: none">
Angle:
<select id="radial_angle">
<option value=0>Final</option>
<option value=1>Initial</option>
<option value=2>Average</option>
</select>
<br>
Decomposition:
<select id="radial_decomposition">
<option value=0>Smooth</option>
<option value=1>Discrete</option>
</select>
</div>
<hr>
Colouring:
<select id="esc_exterior_colouring">
<option value=0>Gradient</option>
<option value=1>Hue</option>
</select>
<hr>
<canvas id="exterior_gradient" class="gradient" data-init_min_colour="#FFFFFF" data-init_max_colour="#0000FF"></canvas>
</details>
<details>
<summary>
Interior colouring
</summary>
Style:
<select id="interior_colouring">
<option value=0>Solid</option>
<option value=1>Average Magnitude</option>
<option value=2>Min Dist</option>
<option value=3>Total Orbit Dist</option>
<option value=4>Stripe Average</option>
<option value=6>Period Checking</option>
<option value=7>CodeParade</option>
<option value=5>Orbit Trap</option>
</select>
<div id="interior_stripe_div" style="display: none">
Density:
<input id="interior_stripe_density" type=number value=3.0 min=0 step=0.1>
</div>
<div id="interior_period_div" style="display: none">
Max period length:
<input id="interior_period_length" type=number value=10 min=0>
<br>
Threshold:
<input id="interior_period_threshold" type=number value=0.00001 min=0 step="0.00001">
</div>
<hr>
<div style="display: grid">
<div id="interior_solid_div">
<div class="grid-entry">
Colour:
<input id="interior_solid_colour" type=color value=#000000>
</div>
</div>
<div id="interior_dist_div" style="display: none">
<div class="grid-entry">
Close Colour:
<input id="interior_close_colour" type=color value=#000000>
</div>
<div class="grid-entry">
Far Colour:
<input id="interior_far_colour" type=color value=#FF00FF>
</div>
</div>
</div>
</details>
</div>
<div id="lyapunov_options" style="display: none">
<details open=true>
<summary>
Chaotic map options
</summary>
Map:
<select id="lya_fractal_type">
<option value=0>Logistic</option>
<option value=1>Gaussian</option>
<option value=2>Circle</option>
<option value=3>Polynomial</option>
<option value=4>Exponent Logistic</option>
<option value=5>Squared Sine Logistic</option>
<option value=6>Sine</option>
<option value=7>Cosine</option>
<option value=8>Hyperbolic Cosine</option>
<option value=9>Exponential</option>
</select>
<div id="lya_function_text" style="font-family: monospace">
x ← rx(1 - x)
</div>
<div id="lya_gauss_div" style="display: none">
α:
<input id="lya_gauss_alpha" type=number value=4 min=0 max=10 step=0.1>
</div>
<div id="lya_circle_div" style="display: none">
Ω:
<input id="lya_circle_omega" type=number value=0.33 min=0 max=1 step=0.01>
</div>
<div id="lya_quadratic_div" style="display: none">
a:
<input id="lya_quadratic_a" type=number value=1 min=-4 max=4 step=0.1>
</div>
<div id="lya_exponent_div" style="display: none">
p:
<input id="lya_exponent" type=number value=2 step=0.1>
</div>
<div id="lya_squared_sine_div" style="display: none">
μ:
<input id="lya_squared_sine_mu" type=number value=0.2 min=0 max=1 step=0.01>
</div>
<div id="lya_trig_div" style="display: none">
θ:
<input id="lya_trig_theta" type=number value=0.0 min=0 max=3.14 step=0.01>
</div>
<div id="lya_cosh_div" style="display: none">
a:
<input id="lya_cosh_a" type=number value=2 min=1 max=5 step=0.01>
</div>
</details>
<details open=true>
<summary>
Sequence
</summary>
Sequence (X, Y, and Z only):
<input id="lya_sequence" type=text value="XY" maxlength=8 size=8>
<br>
Z value:
<input id="z_value" type=range min=0.5 max=4.5 value=2.5 step=0.005 style="width:95%">
<hr>
Initial Value:
<input id="lya_initial" type=number value=0.5 step=0.1>
</details>
<details open=true>
<summary>
Iteration parameters
</summary>
Iterations:
<input id="lya_iterations" type=number value=300 min=0 step=50>
</details>
<details open=true>
<summary>
Colouring
</summary>
<div style="display: grid">
<div class="grid-entry">
Stable:
<input id="stable_colour" type=color value=#FFFF00>
</div>
<div class="grid-entry">
Chaotic:
<input id="chaotic_colour" type=color value=#0000FF>
</div>
<div class="grid-entry">
Infinity:
<input id="infinity_colour" type=color value=#000000>
</div>
</div>
</details>
</div>
<div id="root_finding_options" style="display: none">
<details open=true>
<summary>
Function options
</summary>
Function:
<select id="rtf_function">
<option value=0>Cubic</option>
<option value=1>Sine</option>
<option value=2>General Exponent</option>
</select>
<br>
Algorithm:
<select id="rtf_algorithm">
<option value=0>Newton</option>
<option value=1>Halley</option>
<option value=2>Schröder</option>
<option value=5>Householder-3</option>
<option value=4>Secant</option>
<option value=3>Steffensen</option>
</select>
<div id="secant_div" style="display: none">
<br>
Starting point:
<select id="secant_start">
<option value=0>z0 = 0</option>
<option value=1>z0 = swap(z)</option>
<option value=2>z0 = 2z</option>
<option value=3>z0 = conj(z)</option>
<option value=4>z0 = z²</option>
</select>
</div>
<hr>
Fractal Type:
<select id="rtf_fractal_type">
<option value=0>Classic</option>
<option value=1>Nova</option>
<option value=2>Nova Julia</option>
<option value=3>Meta Convergence</option>
</select>
</details>
<details open=true>
<summary>
Fun movables
</summary>
<div id="root_selector_div">
Roots:
<br>
<canvas id="root_selector" class=selector width=200px height=200px></canvas>
<hr>
</div>
<div id="rtf_exponent_div" style="display:none">
<div id="rtf_exponent_text" class="complex-text">
p: 3 + 0i
</div>
<canvas id="rtf_exponent_selector" class=selector width=200px height=200px></canvas>
<hr>
</div>
<div>
<div id="a_text" class="complex-text">
a = 1 + 0i
</div>
<canvas id="a_selector" class="selector" width=200px height=200px></canvas>
<hr>
</div>
<div id="rtf_julia_div" style="display: none">
<div id="rtf_julia_text" class="complex-text">
c = 0 + 0i
</div>
<canvas id="rtf_julia_c_selector" class="selector" width=200px height=200px></canvas>
</div>
</details>
<details open=true>
<summary>
Iteration options
</summary>
Max Iterations:
<input id="rtf_iterations" type=number value=40 min=0>
<br>
Bailout Threshold:
<input id="rtf_threshold" type=number value=0.01 min=0 step=0.01 style="width: 70px">
</details>
<details open=true>
<summary>
Colouring style
</summary>
Style:
<select id="rtf_colouring_type">
<option value=0 id="rtf_root_colouring">Root</option>
<option value=1 id="rtf_shaded_root_colouring" >Shaded Root</option>
<option value=5 id="rtf_auto_root_colouring">Auto Root</option>
<option value=2 id="rtf_convergence_colouring">Convergence</option>
<option value=3 id="rtf_max_orbit_dist_colouring">Max Orbit Distance</option>
<option value=4 id="rtf_closest_root_dist_colouring">Closest Root Distance</option>
</select>
<div id="rtf_dist_options" style="display: none">
Modulo:
<input id="rtf_dist_mod" type=number value=2 min=0.1 max=10 step=0.1>
</div>
<div id="rtf_root_dist_options" style="display: none">
Brightness:
<input id="rtf_root_dist_brightness" type=number value=2 min=0.1 max=10 step=0.1>
</div>
</details>
<details open=true>
<summary>
Colouring
</summary>
<div id="root1_colour_div" class="grid-entry">
Root 1 Colour:
<input id="root1_colour" type=color value=#FF0000>
</div>
<div id="root2_colour_div" class="grid-entry">
Root 2 Colour:
<input id="root2_colour" type=color value=#00FF00>
</div>
<div id="root3_colour_div" class="grid-entry">
Root 3 Colour:
<input id="root3_colour" type=color value=#0000FF>
</div>
<div id="convergent_colour_div" class="grid-entry" style="display: none">
Convergent Colour:
<input id="convergent_colour" type=color value=#FFFFFF>
</div>
<div class="grid-entry">
Unconvergent Colour:
<input id="base_colour" type=color value=#000000>
</div>
</details>
</div>
<div id="pendulum_options" style="display: none">
<details open=true>
<summary>
Iteration parameters
</summary>
Iterations:
<input id="pend_iterations" type=number value=200 min=0 step=10>
<br>
Friction:
<input id="pend_friction" type=number value=0.01 min=0 step=0.001>
<br>
Tension:
<input id="pend_tension" type=number value=0.75 min=0 step=0.01>
<br>
Pendulum Mass:
<input id="pend_mass" type=number value=1.0 min=0 step=0.01>
<br>
dt:
<input id="pend_dt" type=number value=0.02 min=0 step=0.001>
</details>
<details id="magnets" style="display: grid" open=true>
<summary>
Magnets
</summary>
<canvas id="magnet_selector" class=selector width=200px height=200px></canvas>
<button onclick="PENDULUM.addMagnet(true)">
Add
</button>
<button onclick="PENDULUM.deleteMagnet()">
Delete
</button>
</details>
<details open=true>
<summary>
Colouring Options
</summary>
Colouring Style:
<select id="pend_colouring_style">
<option value=0>Closest Magnet</option>
<option value=1>Shaded Closest</option>
</select>
Base Colour:
<input id="pend_base_colour" type=color value=#000000>
</details>
</div>
<div id="recursive_options" style="display: none">
<details open=true>
<summary>
Fractal options
</summary>
Fractal Type:
<select id="rc_fractal_type">
<option value=0>Sierpiński Carpet</option>
<option value=1>Sierpiński Triangle</option>
<option value=2>T-square</option>
<option value=3>Pythagoras Tree</option>
<option value=4>H Tree</option>
<option value=5>Vicsek</option>
</select>
</details>
<details open=true>
<summary>
Iteration options
</summary>
Iterations:
<input id="rc_iterations" type=number value=8 min=0 max=20>
</details>
</div>
</div>
<div class="sidebar">
<details>
<summary>
Transformations
</summary>
Transformation:
<select id="transformation">
<option value=0>None</option>
<option value=1>Invert</option>
<option value=2>Möbius</option>
<option value=3>Exponent</option>
<option value=4>Polar</option>
</select>
<div id="invert_div" style="display: none">
<div id="invert_text" class="complex-text">
0 + 0i
</div>
<canvas id="invert_selector" class="selector" width=200px height=200px></canvas>
</div>
<div id="moebius_div" style="display: none">
<div id="moebius_a_text" class="complex-text">
a = 0 + 0i
</div>
<canvas id="moebius_a_selector" class="selector" width=200px height=200px></canvas>
<div id="moebius_b_text" class="complex-text">
b = 0 + 0i
</div>
<canvas id="moebius_b_selector" class="selector" width=200px height=200px></canvas>
<div id="moebius_c_text" class="complex-text">
c = 0 + 0i
</div>
<canvas id="moebius_c_selector" class="selector" width=200px height=200px></canvas>
<div id="moebius_d_text" class="complex-text">
d = 0 + 0i
</div>
<canvas id="moebius_d_selector" class="selector" width=200px height=200px></canvas>
</div>
<div id="trans_exponent_div" style="display: none">
<div id="trans_exponent_a_text" class="complex-text">
a = 1 + 0i
</div>
<canvas id="trans_exponent_a_selector" class="selector" width=200px height=200px></canvas>
<div id="trans_exponent_b_text" class="complex-text">
b = 0 + 0i
</div>
<canvas id="trans_exponent_b_selector" class="selector" width=200px height=200px></canvas>
</div>
</details>
<details>
<summary>
Animations
</summary>
Frame delay:
<input id="animation_frame_delay" type=number value=50 min=5 step=1 style="width: 40px">ms
<br>
Duration:
<input id="animation_duration" type=number value=5 min=0.5 step=0.5>s
<br>
Speed:
<input id="animation_speed" type=number value=1 min=0.1 step=0.1 style="width: 40px">x
<hr>
<select id="esc_animations">
<optgroup label="Julia">
<option value=0>Circular walk</option>
<option value=1>Spiral walk</option>
</optgroup>
</select>
<div>
Radius:
<input type=number value=1 min=0 step=0.1 anim_param=1>
</div>
<button onclick="playAnimation()">
Play
</button>
</details>
<details open=true>
<summary>
Global view options
</summary>
Samples/pixel:
<input id="samples" type=number value=1 min=1>
<br>
Blending:
<select id="blending_algorithm" value=1>
<option value=0>RGB</option>
<option value=1>RGB Square</option>
<option value=4>HSV</option>
<option value=2>XYZ</option>
<option value=3>LAB</option>
</select>
<hr>
Canvas Size:
<select id="canvas_size" value=1000>
<option value=600>600x600</option>
<option value=800>800x800</option>
<option value=1000 selected>1000x1000</option>
<option value=1200>1200x1200</option>
<option value=1400>1400x1400</option>
<option value=1600>1600x1600</option>
</select>
<hr>
<div id="display_text" style="font-family: monospace">
z = 0 + 0i
<br>
zoom = 0.5
</div>
<button onclick="resetView()">
Reset View
</button>
</details>
<details open=true>
<summary>
Notes
</summary>
WASD = Move <br>
+/- = Zoom
<hr>
Don't expect every feature to <br>
play well with every other feature!<br>
<a href="sources.html">Sources</a>
</div>
</div>
</div>
<input id="colour-picker" type=color tabindex=-1 style="display: none">
</body>
</html>