### PULSATING & SWEEPING ROSE PATTERN
## Built by Vampyrium
## Ver. 1.0.1.1 2017-10-14 12:28 PM EDT
## Use with rectangular coordinates, AT LEAST 200 beams (20 x 10) for best results

## VAMPYRIUM'S NOTES
## "fraction" is not used here due to its range of [0,1]. Since we're working
## with angles and a design that loops here, that has the potential of causing
## two beams to shine in the same spot at the "beginning"/"end" where the
## design loops. The "relindex" implementation below obviates this issue.
##
## The laser expression feature as a whole is meant for exploration and
## experimentation, but if you don't know what you're doing, just try
## changing the values in the "Configuration" section. If using whole
## numbers for "k", try a maxangle of 2*pi (or tau) for even numbers and pi for
## odd numbers.
##
## Much more information on rose graphs can be found here, if you're so inclined:
## https://en.wikipedia.org/wiki/Rose_(mathematics)

# Initialization
relindex = index/count;

## CONFIGURATION OPTIONS
## time_offset:         Used for changes over time (color changes, sweep effect)
## k and c:             Changes the pattern's shape (refer to Wikipedia link)
##                      For c, the default value is an equation using the
##                      time_offset to create a slight pulsating effect.
## size:                Scales the pattern up or down (default: 100)
## maxangle:            Max value of theta in parametric equations. Adjust if
##                      pattern is incomplete or if beams are overlapping.
## color_hue_width:     Span of hue values being shown at once
## color_change_speed:  Speed of the color changing effect
## sweep_effect_factor: Higher factors lead to tighter and more numerous bands
##                      in the sweeping effect.
## sweep_speed:         Speed of the sweeping effect

# Configuration
time_offset = time;
k = 0.4;
c = cos(time_offset) * 0.05;
size = 100;
maxangle = pi * 10;
color_hue_width = 120;
color_change_speed = 120;
sweep_effect_factor = pi * 8;
sweep_speed = 3;


# Masks
firsthalf = (relindex < 0.5);
lasthalf = (firsthalf < 1);

# Expression
relangle = relindex * maxangle;
size_cos_k_relangle_c = (size * cos(k * relangle)) + c;
x' = size_cos_k_relangle_c * cos(relangle);
y' = size_cos_k_relangle_c * sin(relangle);

h = (((relindex * firsthalf) + ((1-relindex) * lasthalf)) * color_hue_width) + (time_offset * color_change_speed);
s = 1;
v = ((cos((relindex * sweep_effect_factor) + (time_offset * sweep_speed))) / 2) + 0.5;