The LaserBoy Thread

[lasermaster1977]

In your example, 3 and 5 are the amplitude. 0 and 90 are phase.

It's worth noting that since this all gets scaled to fit inside of short integer space, the actual size of a figure is more or less irrelevant except when compared to other figures in the same space. Offset is also typically factored out unless you normalize with the origin. So there are literally an infinite number of ways to make the same final results.

Not to mention that frequency is directly related to time, so different combinations of frequency and duration can also yield the same results.

LBO(t) == amplitude * function(t * frequency + phase) * e ^ (-damping / t) + offset

duty_cycle is a parameter that has no representation in the above expression. It actually changes the character of function. The value of duty_cycle must be between 0.0 and 1.0. A value of 0.5 is 50%. The sin function has 50% above and 50% below its zero value.

In case you're wondering, Yes. I have had to scrape my brains off the ceiling several times while developing this code.

I love that! New discoveries are what really drive me to keep working on this. And working with other people is the biggest reward.

my bad, for being in a hurry. I meant
x=sin(3x) + sin(5x), y=cos(3x) + cos(5x)
for x = 0 to 360

[james]

#math phase_cycle        360.0
#math interval_cycle     1.0

#math  start             0.0
#math  duration          1.0
math  iterations        1000

# x = sin(t * 3) + sin(t * 5)
# y = cos(t * 3) + cos(t * 5)
# for t = 0 to two_pi

math  LBO1 frequency    3.0

math  LBO2 frequency    5.0

math  LBO3 frequency    3.0
math  LBO3 phase        90.0

math  LBO4 frequency    5.0
math  LBO4 phase        90.0

# https://en.wikipedia.org/wiki/Harmonograph
#    x = LBO1(t) + LBO2(t)
#    y = LBO3(t) + LBO4(t)
math  harmonograph

math  render

[james]

There are some other features in the new development version that are worth mentioning.

If you go into the u menu for user interface visual attributes, you can now turn vector rendering on or off. This is the line between two consecutive vertices. With it off all you see are the vertices themselves.

Also, in the [Tab] menu option 4 display settings, option 1 is rendered line width in pixels. So now you can make your vector lines as thick as you want.

Set it to something like 4 to 7 and then load this:

#################################################
#
#   This file was written by James Lehman.
#   creator of LaserBoy,
#
#   the free, multiplatform laser display
#   application that reads this format.
#
#   <james@akrobiz.com>
#   Extra Stimulus Inc., Akron, Ohio USA
#   http://laserboy.org/
#
#   ASCII format version: LaserBoy-txt-04-21-2021
#
#################################################

#math phase_cycle        360.0
#math rotation_cycle     1.0
#math interval_cycle     1.0

math hues_span_factor   1.0
math hues_shift         3

math frames             1000

math  start             0.0
math _start             0.0

math  duration          100.0
math _duration          100.0

math  iterations        96
math _iterations        303

math  LBO1  phase       90.0
math _LBO1  phase       90.0

#----------------------------------------------
# https://en.wikipedia.org/wiki/Lissajous_curve
#    x = LBO1(t)
#    y = LBO2(t)
math _oscillator_xy

math  factor         0.0  0.0  0.0
math  factor_        1.0  1.0  1.0
math  scale_acceleration  0.0
math  spread_scale

math  color_span_hues
math  reverse_vectors
math  render

###############################################
###############################################

After it's loaded, get back to the main menu and hit the ` key (just to the left of the digit 1 on the top row) to play the animation.