turtles-own [ col               ;sets color of an explosion particle
  x-vel             ;x-velocity
  y-vel             ;y-velocity
  z-vel             ;z-velocity
]

globals [initial-x-vel initial-y-vel initial-z-vel current-material max-cor m i value step-size current-box-x current-box-y t seed-x-vel seed-z-vel ]

breed [ drones drone ]
breed [ seeds seed ]
breed [ bisectors bisector ]

extensions [array matrix]
patches-own [material]

drones-own [ terminal-y-vel ] ;velocity at which drone will explode
seeds-own [ dim ]              ;used for fading particles

;SETUP
;-----
;This function clears the graphics window of all patches and turtles.

to setup
  clear-all
  reset-ticks
  launch-drones
  generate-matrix
end

;GO
;--
;If there are no turtles, then it creates a random number
;according to the slider FIREWORKS and sets all the initial
;values for each firework.
;It then calls PROJECTILE-MOTION, which launches and explodes the fireworks.

to go
  ;we don't want the model to run too quickly because otherwise,
  ;you wouldn't be able to see the fireworks
  every 0.06
  [
    if spin-observer?
      [ orbit-right 2 ]
  ]
  every 0.05
  [
    fall-down
    display
  ]
  if not any? turtles
  [ tick ]
end

to launch-drones
  clear-drawing
  create-drones 2
  [ setxyz 0 20 0
    set roll 0
    set shape "box"
    set size 0.1
    set x-vel initial-x-vel
    set z-vel initial-z-vel
    set y-vel 0
    set col one-of base-colors    ;; choose a random 'primary' color   i.e. 5, 15, 25, etc.
    set color (col + 2)
    set size 2
    set terminal-y-vel -10     ;; at what speed does the drone explode?
  ]

end

to move-to-point [target-x target-z]
  ask drones [
    set initial-x-vel (target-x - xcor)
    set initial-z-vel (target-z - zcor)
  ]

end

to fall-down
  ask drones [
    if manual_controls? [
      move-to-point new-x new-z
    ]
    set x-vel initial-x-vel
    set z-vel initial-z-vel
    projectile-motion
  ]
  ask seeds [ projectile-motion-seed ]
end

;PROJECTILE-MOTION
;-----------------
;This function simulates the actual free-fall motion of the turtles.
;If a turtle is a drone it checks if it has slowed down enough to explode.

to projectile-motion-seed               ;; turtle procedure
  set y-vel (y-vel - (gravity / 5))
  let temp-y ycor + (y-vel / 10)
  while [ycor > temp-y] [
    setxyz xcor round(ycor - 1) zcor
    kill-wrapped
  ]
  ifelse (breed = drones)
    [ if (y-vel < terminal-y-vel)
      [ explode
        die ]
  ]
  [ fade ]
end

to generate-matrix

  let a array:from-list n-values 3 [0]

  set value 3
  set i 0

  repeat 3 [
    array:set a i value
    set value ((value * 2) - 1)
    set i i + 1
  ]

  set value ((value + 1) / 2)

  let n-rows value
  let n-cols value
  let initialValue 0
  set m matrix:make-constant n-rows n-cols initialValue


  matrix:set m 0 0 (random 8) + random 3
  matrix:set m 0 (value - 1) (random 8) + random 3
  matrix:set m (value - 1) 0 (random 8) + random 3
  matrix:set m (value - 1) (value - 1) (random 8) + random 3

  set value value - 1


  let half_value (value / 2)


  let loop_count 3
  let counter 2 ^ (loop_count)


  repeat 3 [
    let tempy 0
    set i 0
    let j 0
    while[i <= (counter + 1)] [
      let tempx 0
      set j 0
      while[j <= (counter + 1)] [
        carefully [
          steps value tempx tempy half_value
        ] []
        set tempx tempx + counter
        set j j + 1
      ]
      set tempy tempy + counter
      set i i + 1
    ]
    set loop_count loop_count - 1
    set counter 2 ^ (loop_count)
    set value half_value
    set half_value (value / 2)
  ]


  print-matrix
end

to diamond_step[step_size starting_value_x starting_value_y]
  let half_step_size (step_size / 2)
  let val1 matrix:get m starting_value_x starting_value_y
  let val2 matrix:get m (starting_value_x + step_size) starting_value_y
  let val3 matrix:get m starting_value_x (starting_value_y + step_size)
  let val4 matrix:get m (starting_value_x + step_size) (starting_value_y + step_size)

  let summation ((val1 + val2 + val2 + val4) / 4)

  matrix:set m (starting_value_x + half_step_size) (starting_value_y + half_step_size) floor(summation)

end

to square_step[step_size starting_value_x starting_value_y]
  let half_step_size (step_size / 2)

  let summation 0
  let num_additions 0

  carefully [
    let val1 matrix:get m (starting_value_x + half_step_size) starting_value_y
    set summation summation + val1
    set num_additions num_additions + 1
  ] []

  carefully [
    let val2 matrix:get m (starting_value_x - half_step_size) starting_value_y
    set summation summation + val2
    set num_additions num_additions + 1
  ] []

  carefully [
    let val3 matrix:get m starting_value_x (starting_value_y + half_step_size)
    set summation summation + val3
    set num_additions num_additions + 1
  ] []

  carefully [
    let val4 matrix:get m starting_value_x (starting_value_y - half_step_size)
    set summation summation + val4
    set num_additions num_additions + 1
  ] []

  set summation (summation / num_additions)

  matrix:set m starting_value_x starting_value_y floor(summation)
end

to steps[step_size starting-x starting-y half-value]
  diamond_step step_size starting-x starting-y
  square_step step_size starting-x (starting-y + half-value)
  square_step step_size (starting-x + half-value) starting-y
  square_step step_size (starting-x + step_size) (starting-y + half-value)
  square_step step_size (starting-x + half-value) (starting-y + step_size)

end




to print-matrix
  set i 0
  let j 0
  while [i < (9)] [
    while [j < (9)] [
      let temp-material one-of ["rock" "tree" "tree" "tree" "dirt"  "dirt"  "dirt"  "dirt"  "dirt" "dirt"  "dirt"  "dirt"  "dirt"  "dirt"]
      ask patches with [(pxcor = i) and (pycor <= (matrix:get m i j)) and (pzcor = j)] [
        set material temp-material
        if material = "tree" [
          set pcolor 62
        ]
        if material = "rock" [
          set pcolor gray
        ]
        if material = "dirt" [
          set pcolor brown
        ]
      ]
      set j j + 1
    ]
    set i i + 1
    set j 0
  ]

end

to projectile-motion
  let tempx1 xcor
  let tempy1 ycor
  let tempz1 zcor
  setxyz round(xcor + (x-vel)) round(ycor + (y-vel)) round(zcor + (z-vel))

  let tempx2 xcor
  let tempy2 ycor
  let tempz2 zcor
  if ((tempx1 != tempx2) or (tempy1 != tempy2) or (tempz1 != tempz2)) [
    explode
  ]
end

;EXPLODE
;-------
;This is where the explosion is created.
;EXPLODE calls hatch a number of times indicated by the slider seedMENTS.

to explode                 ;; turtle procedure
  set seed-x-vel 0
  set seed-z-vel 0
  hatch-seeds 1
  [ set dim 0
    set size .5
    set shape "circle"
    tilt-up asin (1.0 - random-float 2.0)
    roll-right random-float 360
    set x-vel seed-x-vel
    set z-vel seed-z-vel
    set y-vel -30
  ]
end


;FADE
;----
;This function changes the color of a seed.
;Each seed fades its color by an amount proportional to FADE-AMOUNT.

to fade
end


;KILL-WRAPPED
;--------
;This function is used to keep the turtles within the vertical bounds of the world.
;If they go above or below the top or bottom of the world kill them.

to kill-wrapped
  ask patch-here
  [
    set current-material material
  ]
  if (current-material = "dirt") [
    ask patch-here [
      set pcolor green
    ]
    die
  ]
  if ((ycor - 1) < 0) [
    die
  ]
end

to do
  split-terrain
  plant-seeds 0 0 1
end

to split-terrain
  ask patch 0 15 0
  [
    set pcolor red
    sprout-bisectors 1 [
      set hidden? true
    ]
  ]
  ask patch (max-pxcor / 2) 15 (max-pzcor / 2)
  [
    sprout-bisectors 1 [
      set hidden? true
    ]
  ]
  ask patch max-pxcor 15 max-pzcor
  [
    set pcolor red
    sprout-bisectors 1 [
      set hidden? true
    ]
  ]
  ask bisectors [
    create-links-with other bisectors
  ]
end

to plant-seeds [start-x start-z counter]
  ask patches with [(pxcor = start-x) and (pzcor = start-z) and (material != 0) and ([pcolor] of patch pxcor (pycor + 1) pzcor = black)]  [
    ask min-one-of (patches with [(material = "dirt") and (pzcor != pxcor) and ([pcolor] of patch pxcor (pycor + 1) pzcor = black) and (distance myself > 2) and (count patches in-radius 2 with [pcolor = green] <= 1)]) [distance myself] [
      set pcolor green
      sprout 1 [
        set ycor 15
        if count turtles-here > 1 [die]
      ]
      set start-x pxcor
      set start-z pzcor
      set counter counter + 1
      if counter = 1000 [
        ask patches with [pcolor = green] [set pcolor brown]
        stop
      ]
      plant-seeds start-x start-z counter
    ]
  ]
end

to cast
  every .05 [
    let location1 0
    let location2 0
    carefully [
      ask drone 0 [
        set location1 who
      ]
    ] []
    carefully [
      ask drone 1 [
        set location2 who
      ]
    ] []
    carefully[
      ask min-one-of turtles with [(shape = "default") and (xcor > zcor)] [distance turtle location1] [
        let temp-x xcor
        let temp-z zcor
        ask drone 0 [
          set initial-x-vel (temp-x - xcor)
          set initial-z-vel (temp-z - zcor)
          fall-down
        ]
        die
      ]
    ] [
      carefully [ask drone 0 [die]] []
    ]
    carefully[
      ask min-one-of turtles with [(shape = "default") and (xcor < zcor)] [distance turtle location2] [
        let temp-x xcor
        let temp-z zcor
        ask drone 1 [
          set initial-x-vel (temp-x - xcor)
          set initial-z-vel (temp-z - zcor)
          fall-down
          display
        ]
        die
      ]
    ] [
      carefully [ask drone 1 [die]] []
    ]
  ]
end
; Copyright 2006 Uri Wilensky.
; See Info tab for full copyright and license.
@#$#@#$#@
GRAPHICS-WINDOW
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0
89
288
-1
-1
9.0
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10
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1
1
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ticks
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BUTTON
76
76
156
109
setup
setup
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T
OBSERVER
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BUTTON
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76
237
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go
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T
1
T
OBSERVER
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NIL
NIL
NIL
0

SLIDER
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288
184
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gravity
gravity
0.0
3.0
0.7
0.1
1
NIL
HORIZONTAL

BUTTON
401
150
502
183
x-speed-up
set initial-x-vel (initial-x-vel + .5)
NIL
1
T
OBSERVER
NIL
W
NIL
NIL
1

BUTTON
401
183
503
216
x-slow-down
set initial-x-vel (initial-x-vel - .5)
NIL
1
T
OBSERVER
NIL
S
NIL
NIL
1

BUTTON
501
150
595
183
z-speed-up
set initial-z-vel (initial-z-vel + .5)
NIL
1
T
OBSERVER
NIL
E
NIL
NIL
1

BUTTON
500
183
595
216
z-slow-down
set initial-z-vel (initial-z-vel - .5)
NIL
1
T
OBSERVER
NIL
D
NIL
NIL
1

INPUTBOX
403
261
501
321
new-x
0.0
1
0
Number

INPUTBOX
501
261
600
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new-z
0.0
1
0
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BUTTON
66
132
182
165
Every 2 meters
if timer > .5 [\nset new-x new-x + 2\nif new-x > 8 [\nset new-x 0\nset new-z new-z + 2\n]\nif new-z > 8 [\nset new-z 0\nstop\n]\nreset-timer\n]
T
1
T
OBSERVER
NIL
NIL
NIL
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1

SWITCH
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286
338
319
spin-observer?
spin-observer?
1
1
-1000

TEXTBOX
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119
551
141
Manual Controls
18
0.0
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TEXTBOX
403
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571
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Coordinate Controls
18
0.0
0

TEXTBOX
70
335
184
390
^ Strength of Gravity\nNot a huge factor but can be made bigger if necessary
11
0.0
1

SWITCH
187
324
341
357
Manual_Controls?
Manual_Controls?
0
1
-1000

BUTTON
186
133
298
166
divide the load
cast
T
1
T
OBSERVER
NIL
NIL
NIL
NIL
1

MONITOR
431
412
643
457
NIL
count patches with [pcolor = green]
17
1
11

@#$#@#$#@
## WHAT IS IT?

This program models the action of fireworks.  Rockets begin at the bottom of the world, shoot upwards into the sky and then explode, emitting showers of falling sparks.

## HOW IT WORKS

Each rocket, represented by a turtle, is launched upward with an initial x y and z velocity.  At a certain point in the sky, an explosion occurs, which is represented by a series of turtle hatches.  Each hatched turtle inherits the velocity from the original rocket in addition to velocity from the explosion itself.  The result is a simulation of a fireworks display.

## HOW TO USE IT

SETUP creates FIREWORKS rockets at the bottom of the screen (MIN-PZCOR). Pressing the GO forever button executes the model continually, launching the rockets. When a rocket hits its peak velocity, it explodes into FRAGMENTS pieces.

GRAVITY determines the gravitational strength in the environment.  A larger value will give a greater gravitational acceleration, meaning that particles will be forced to the ground at a faster rate.  The inverse is true for smaller values.

INITIAL-X-VEL sets the initial x-velocity of each rocket to a random number between the negative and positive value of the number indicated on the slider.

INITIAL-Y-VEL sets the initial y-velocity of each rocket to a random number between the negative and positive value of the number indicated on the slider.

INITIAL-Z-VEL sets the initial z-velocity of each rocket to a random number between 0 and the number indicated on the slider plus ten.  This is to ensure that there is a range of difference in the initial z-velocities of the fireworks.

FADE-AMOUNT determines the rate at which the explosion particles fade after the explosion.

If TRAILS? is true the fragments of each explosion will have their pens down so the paths of each fragment are visible (and they look like real fireworks).

If SPIN-OBSERVER? is on the Observer will spin around the world as the model runs.

The model will launch a new set of rockets every DELAY seconds.

This model has been constructed so that all changes in the sliders and switches will take effect in the model during execution.  So, while the GO button is still down, you can change the values of the sliders and the switch, and you can see these changes in the world.

## THINGS TO NOTICE

Experiment with the INITIAL-X-VEL, INITIAL-Y-VEL, and INITIAL-Z-VEL sliders.  Observe that initial x and y velocities of zero launch the rockets straight upwards.  When the initial x or y velocities are increased, notice that some rockets make an arc in the sky.

With the initial z-velocity, observe that, on a fixed GRAVITY value, the heights of the fireworks are lower on smaller initial z-velocities and higher on larger ones.  Also observe that each rocket explodes at a height equal to or a little less than its apex.

## THINGS TO TRY

Observe what happens to the model when the GRAVITY slider is set to different values.  Watch what happens to the model when GRAVITY is set to zero.  Can you explain what happens to the fireworks in the model?  Can you explain why this phenomenon occurs?  What does this say about the importance of gravity?  Now set the GRAVITY slider to its highest value.  What is different about the behavior of the fireworks at this setting?  What can you conclude about the relationship between gravity and how objects move in space?

## EXTENDING THE MODEL

The fireworks represented in this model are only of one basic type.  A good way of extending this model would be to create other more complex kinds of fireworks.  Some could have multiple explosions, multiple colors, or a specific shape engineered into their design.

## NETLOGO FEATURES

An important aspect of this model is the fact that each particle from an explosion inherits the properties of the original firework.  This informational inheritance allows the model to adequately represent the projectile motion of the firework particles since their initial x, y, and z velocities are relative to their parent firework.

To visually represent the fading property of the firework particles, this model made use of the reporter `scale-color`.  As the turtle particles fall to the ground, they hold their pens down and gradually scale their color to black.  As mentioned above, the rate of fade can be controlled using the FADE-AMOUNT slider.

## HOW TO CITE

If you mention this model or the NetLogo software in a publication, we ask that you include the citations below.

For the model itself:

* Wilensky, U. (2006).  NetLogo Fireworks 3D model.  http://ccl.northwestern.edu/netlogo/models/Fireworks3D.  Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

Please cite the NetLogo software as:

* Wilensky, U. (1999). NetLogo. http://ccl.northwestern.edu/netlogo/. Center for Connected Learning and Computer-Based Modeling, Northwestern University, Evanston, IL.

## COPYRIGHT AND LICENSE

Copyright 2006 Uri Wilensky.

![CC BY-NC-SA 3.0](http://ccl.northwestern.edu/images/creativecommons/byncsa.png)

This work is licensed under the Creative Commons Attribution-NonCommercial-ShareAlike 3.0 License.  To view a copy of this license, visit https://creativecommons.org/licenses/by-nc-sa/3.0/ or send a letter to Creative Commons, 559 Nathan Abbott Way, Stanford, California 94305, USA.

Commercial licenses are also available. To inquire about commercial licenses, please contact Uri Wilensky at uri@northwestern.edu.

This is a 3D version of the 2D model Fireworks.

<!-- 2006 3D -->
@#$#@#$#@
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Polygon -7500403 true true 135 105 90 60 45 45 75 105 135 135
Polygon -7500403 true true 165 105 165 135 225 105 255 45 210 60
Polygon -7500403 true true 135 90 120 45 150 15 180 45 165 90

square
false
0
Rectangle -7500403 true true 30 30 270 270

square 2
false
0
Rectangle -7500403 true true 30 30 270 270
Rectangle -16777216 true false 60 60 240 240

star
false
0
Polygon -7500403 true true 151 1 185 108 298 108 207 175 242 282 151 216 59 282 94 175 3 108 116 108

target
false
0
Circle -7500403 true true 0 0 300
Circle -16777216 true false 30 30 240
Circle -7500403 true true 60 60 180
Circle -16777216 true false 90 90 120
Circle -7500403 true true 120 120 60

tree
false
0
Circle -7500403 true true 118 3 94
Rectangle -6459832 true false 120 195 180 300
Circle -7500403 true true 65 21 108
Circle -7500403 true true 116 41 127
Circle -7500403 true true 45 90 120
Circle -7500403 true true 104 74 152

triangle
false
0
Polygon -7500403 true true 150 30 15 255 285 255

triangle 2
false
0
Polygon -7500403 true true 150 30 15 255 285 255
Polygon -16777216 true false 151 99 225 223 75 224

truck
false
0
Rectangle -7500403 true true 4 45 195 187
Polygon -7500403 true true 296 193 296 150 259 134 244 104 208 104 207 194
Rectangle -1 true false 195 60 195 105
Polygon -16777216 true false 238 112 252 141 219 141 218 112
Circle -16777216 true false 234 174 42
Rectangle -7500403 true true 181 185 214 194
Circle -16777216 true false 144 174 42
Circle -16777216 true false 24 174 42
Circle -7500403 false true 24 174 42
Circle -7500403 false true 144 174 42
Circle -7500403 false true 234 174 42

turtle
true
0
Polygon -10899396 true false 215 204 240 233 246 254 228 266 215 252 193 210
Polygon -10899396 true false 195 90 225 75 245 75 260 89 269 108 261 124 240 105 225 105 210 105
Polygon -10899396 true false 105 90 75 75 55 75 40 89 31 108 39 124 60 105 75 105 90 105
Polygon -10899396 true false 132 85 134 64 107 51 108 17 150 2 192 18 192 52 169 65 172 87
Polygon -10899396 true false 85 204 60 233 54 254 72 266 85 252 107 210
Polygon -7500403 true true 119 75 179 75 209 101 224 135 220 225 175 261 128 261 81 224 74 135 88 99

wheel
false
0
Circle -7500403 true true 3 3 294
Circle -16777216 true false 30 30 240
Line -7500403 true 150 285 150 15
Line -7500403 true 15 150 285 150
Circle -7500403 true true 120 120 60
Line -7500403 true 216 40 79 269
Line -7500403 true 40 84 269 221
Line -7500403 true 40 216 269 79
Line -7500403 true 84 40 221 269

x
false
0
Polygon -7500403 true true 270 75 225 30 30 225 75 270
Polygon -7500403 true true 30 75 75 30 270 225 225 270
@#$#@#$#@
NetLogo 3D 6.0.4
@#$#@#$#@
set trails? true
set fireworks 30
setup
repeat 50 [ launch-rockets fall-down ]
@#$#@#$#@
@#$#@#$#@
@#$#@#$#@
@#$#@#$#@
default
0.0
-0.2 0 0.0 1.0
0.0 1 1.0 0.0
0.2 0 0.0 1.0
link direction
true
0
Line -7500403 true 150 150 90 180
Line -7500403 true 150 150 210 180
@#$#@#$#@
0
@#$#@#$#@