Tychos MathJs Language Reference

The following reference guide identifies the language syntax, built in variables, functions, and classes that are used to code your simulations in Tychos. Tychos uses the MathNotepad language. We have included documentation here for some of the helpful functions defined in the MathNotepad language. This is not a complete list of all functions available in MathNotepad, just ones that might be commonly used in Tychos for building scenarios as well as defining goals for those scenarios.
Comments
Comments are statements that you can insert in your code that do not get interpreted and executed by Tychos. To create a comment, you simply indicate a comment by using a hashtag:
# This is a comment.
Variables
To define a variable in Tychos all you need to do is identify a name for the variable. You then type an = sign to assign a value to the variable. The following demonstrates various variable declarations
# Assigns a variable called x the value of 10
x = 10
# Assign a new variable y the value of the x
y = x
# Assign x the value of itself plus 1
x = x + 1
Built-in Scenario Variables
There are a few variables that are built into Tychos. These variables are:
t — How many seconds has passed since this Scenario was started?
dt — Time between frames as seconds, e.g. 0.1 is 1/10th of a second.
frame_count — How many frames have passed? e.g. 1, 2, 3...
X, Y , Z— These are shortcuts for indexing the first two elements of 3-D matrices, e.g. my_particle.pos[X]
Common Math Operators and Functions
These are some common mathematical operators and functions for performing various calculations.
Mathematical Operators
Tychos uses the following operators to perform basic math calculations:
+ — Addition
- — Subtraction
* - Multiplication
/ - Division
^ - Exponent
% - Modulo
Basic Math Functions
You can also use the following basic math functions:
pow(base, power)
The pow(base, power) function takes two arguments, raising the base by the power.
# returns number 8
pow(2,3)
sqrt(positive_number)
The sqrt(positive_number) function takes a single non negative number and returns the real square root of the number.
# returns number 2
sqrt(4)
abs(number)
The abs(number) function returns the absolute value of a number.
# returns number 2
abs(-2)
Trigonometric Functions
The following functions all use radians as the angle measurement. You can use pi to represent PI.
sin(angle)
The sin(angle) function is used to evaluate the trigonometric sine value for a given input angle. The input angle must be provided in radians.
# returns number 1
sin(PI/2)
cos(angle)
The cos(angle) function is used to evaluate the trigonometric cosine value for a given input angle. The input angle must be provided in radians.
# returns number 1
cos(0)
tan(angle)
The tan(angle) function is used to evaluate the trigonometric tangent value for a given input angle. The input angle must be provided in radians.
# returns number 1
tan(PI/4)
asin(value)
The asin(value) function is used to evaluate the trigonometric arcsine value (inverse sine) for a given input. The output angle is given in radians.
# returns number 1.57
asin(1)
acos(value)
The acos(value) function is used to evaluate the trigonometric arccosine value (inverse cosine) for a given input. The output angle is given in radians.
# returns number 0
acos(1)
atan2(X, Y)
The atan2(value) function is used to evaluate the trigonometric arctangent value (inverse tangent) for a given X and Y input. The output angle is given in radians.
# returns number -0.785
atan2(-1, 1)
# returns 2.36
atan2(1, -1)
deg_to_rad(angle)
See below.
radians(angle)
The deg_to_rad(angle) function is not part of the MathNotepad language but is provided as a helper function to make the conversion from degree angles to radians easier. The input is an angle measurement in degrees and the output is the angle measurement in radians.
# returns number .785
deg_to_rad(45)
rad_to_deg(angle)
See below.
degrees(angle)
The degrees(angle) function is not part of the MathNotepad language but is provided as a helper function to make the conversion from radian angles to degrees easier. The input is an angle measurement in radians and the output is the angle measurement in degrees.
# returns number 180
degrees(PI)
Matrix Functions
The following functions provide operations for matrix calculations.
dot(x, y)
Calculates the dot product of two vectors. The dot product of x = [a1, a2, a3, ..., an] and y = [b1, b2, b3, ..., bn] is defined as:
dot(x, y) = a1 * b1 + a2 * b2 + a3 * b3 + … + an * bn
# Work is the dot product of Force (F) and displacement (r)
F = [2, 2]
r = [3, 3]
# returns 12
Work = dot(F, r)
cross
Calculates the cross product for two vectors in three dimensional space. The cross product of x = [a1, a2, a3]and y = [b1, b2, b3] is defined as:
cross(x, y) = [ a2 * b3 - a3 * b2, a3 * b1 - a1 * b3, a1 * b2 - a2 * b1 ]
If one of the input vectors has a dimension greater than 1, the output vector will be a 1x3 (2-dimensional) matrix.
# Torque is the cross product of Force and moment arm (r)
F = [2, 0, 0]
r = [0, 2, 0]
# returns matrix [0, 0, 4]
cross(F, r)
Other Useful Functions
Some other useful functions...
random(min, max)
Return a random number larger or equal to min and smaller than max using a uniform distribution. If now min or max are given, then it returns a random value from 0 to 1. If just one value is given, then it returns a random number between 0 and the input value.
# returns a random number between 0 and 1
random()
# returns a random number between 0 and 100
random(100)
# returns a random number between 30 and 40
random(30, 40)
# returns a 2x3 matrix with random numbers between 0 and 1
random([2, 3])
string(object)
Create a string or convert any object into a string. Elements of Arrays and Matrices are processed element wise.
format(value, precision)
Formats a value into a string. You have several options for how this value will be formatted:
# returns '0.333'
format(1/3, 3)
# returns '21000'
format(21385, 2)
# returns '1200000000'
format(12e8, {notation: 'fixed'})
# returns '2.3000'
format(2.3,  {notation: 'fixed', precision: 4})                
concat(A, B...dim)
Concatenate two or more matrices. This function can also be used to concatenate strings together.
dim: number is a zero-based dimension over which to concatenate the matrices. By default the last dimension of the matrices.
A = [1, 2]
B = [3, 4]
concat(A, B)                  
# returns [1, 2, 3, 4]
math.concat(A, B, 0)           
# returns [[1, 2], [3, 4]]
math.concat('hello', ' ', 'world') 
# returns 'hello world'
drawArrow (deprecated)
This function has been deprecated and you should instead use the class Arrow to represent arrows in your simulations. See below for more details.
The drawArrow function draws an arrow and is commonly used to illustrate vectors for a particle. drawArrow should be called in the Calculations editor because it only draws the arrow for the current frame. If you call drawArrow() in the Initial State editor, you will not see anything.
drawArrow(pos=[0,0], size=[1,0], color="black", components=false, thickness=1) -> returns and draws an Arrow object
pos — coordinates for the starting point of the arrow as an [X,Y] matrix.
size — the vector to illustrate, e.g. [10, 0] will draw an arrow 10 units to the right.
color — Optional HTML color value for your arrow, e.g. "red" or "#ff0000".
components — Optional flag that determines if vector components are drawn, a value of true displays the components.
thickness — Optional stroke value that determines the visual thickness of the arrow.
drawLine (deprecated)
This function has been deprecated and you should instead use the class Line to represent lines in your simulations. See below for more details.
The drawLine function draws a line and is commonly used to illustrate some connecting member like a string or cable, but could really represent anything you like. drawLine should be called in the Calculations editor because it only draws the line for the current frame. If you call drawLine in the Initial State editor, you will not see anything.
drawLine(pos=[0,0], pos2=[10,0], color="black", thickess=1) -> returns and draws an Line object
pos — coordinates for the starting point of the line as an [X,Y] matrix.
pos2 — the coordinates of the end point of the line as an [X,Y] matrix.
color — Optional HTML color value for the line, e.g. "red" or "#ff0000".
thickness — Optional stroke value that determines the visual thickness of the line.
Example — The illustration above was drawn using this command:
# Calculations editor
drawLine([0, 0], [20, 20], "purple", 2)  # a line
drawLine([0, 0], [10, 20], "green", 10)  # another line
unit_vector
This function returns a unit vector representation of the given input vector. Its magnitude is 1 and the direction matches the direction of the input vector. This can be useful if you need just the direction of a vector, but not its magnitude.
unit_vector(vec) -> returns a vector of length 1, and in same direction as vec.
vec - any two dimensional vector as a [X, Y] matrix.
Example:
u = unit_vector([3, 4])  # returns [0.6, 0.8]
magnitude(u)             # returns 1
magnitude
This function returns the scaler magnitude of any given vector. This is helpful when you want to know the length of a vector, for example, if you want the magnitude of a vector, but not its direction.
magnitude(vec) -> returns the scaler magnitude of the vector vec.
vec - any two dimensional vector as a [X, Y] matrix.
Example:
magnitude([3, 4])             # returns 5
direction
This function returns a scalar angle measurement. This is helpful when you want to know the direction of a vector, like the direction of a velocity vector, or the direction of a force vector. The default return angle is given in radians, but can also be expressed in degrees.
direction(vec, units="rad") -> returns the scaler angle measurement of the vector vec heading in radian form or in degree form.
vec - any two dimensional vector as a [X, Y] matrix.
units - optional deg for degree measurement or the default of rad for radians. 
Example:
direction([4, 4])             # returns .785
direction([4, 4], "deg")        # returns 45
polar
This function returns a two-dimensional matrix representing the cartesian components of a polar coordinate corresponding to the magnitude of the radius and the radial angle.
polar(radius, angle, units="rad") -> returns a two dimensional vector as a [X, Y] matrix.
radius - scalar quantity representing the scalar distance of the radius of the 
angle - scalar quantity representing the angle measurement of the polar coordinate.
units - optional deg for degree measurement or the default of rad for radians.
Example:
polar(10, 45, "deg")         # returns [7.07, 7.07]
polar(10, PI/4)            # returns [7.07, 7.07]
getRotatedPosition
This function is simply used for finding a point that has been rotated a given angle about a specific axis. It is just a utility function that could be performed by doing some simple trigonometry calculations, but hey, why not make it easier for you?
getRotatedPosition(point, angle, axis) -> returns a two dimensional vector as a [X, Y] matrix.
point - A vector representing the point that is rotated. 
angle - scalar quantity representing the angle measurement of rotation.
axis - A 2D vector that identifies the axis point about which the position has been rotated.
Example:
getRotatedPosition([10, 0], PI, [0, 0])            # returns [-10, 0]
createPoints
This function creates an array of points based on a domain, a domain increment, and a function expression.
createPoints(min, max, step, expression) -> returns an array of points whose domain is defined from the min value to the max value with an increment defined by step and whose range is evaluated based on the function  expression.
min - the inclusive minimum value of the domain.
max - the exclusive maximum value of the domain.
step - the increment step value of the domain.
expression - a string representing a functional expression that can be evaluated in terms of "x".
Example:
points = createPoints(0, 4, 1, "x^2")
# [[0, 0], [1, 1], [2, 4], [3, 9]]
stop
This function actually evaluates a boolean test and then stops the simulation once the boolean test succeeds. This can be useful if you want the simulation to stop when some condition has been met within your simulation.
stop(test) -> returns a either false or true. If true is returned, the simulation stops.
test - a boolean statement that can be evaluated to true or false. 
Example:
stop(t > 10)             # simulation stops at 10 seconds
stop(buggy.pos[X] == 100) # simulation stops when X position of particle equals 100
Collision Functions
The following functions are meant to help users model collisions more easily. These functions could be used for other purposes rather than modeling collisions as Tychos is not a physics engine. These functions could be thought of as "overlap" functions. They return information about the overlap of objects.
hasCollided
This function returns a boolean true/false value when two objects are given as the source and target. It returns false if the two objects are not determined to be overlapping.
hasCollided(source, target) -> returns a boolean true or false.
source - Circle or Rectangle or Line object 
target - Circle or Rectangle or Line object
Example:
# Initial State
p1 = Circle({pos:[15, 0], radius:10, color:rgba(0, 200, 200, .6)})
b1 = Rectangle({pos:[0, 0], size:[15, 15], color:rgba(200, 0, 200, .6)})
b1.rotate(radians(45))
p3 = Circle({pos:[-15, 0], radius:10, color:rgba(0, 0, 200, .6)})
# Calculations
hasCollided(p1, b1)            # returns true
hasCollided(b1, p3)            # returns true
hasCollided(p1, p3)            # returns false
getIntersect
This function returns a two dimensional matrix representing the minimum translation vector (MTV) that would be needed to separate two objects when they overlap. This can be used to simulate collision forces or to move objects apart based on the magnitude and direction of the MTV.
getIntersect(source, target) -> returns a two dimensional matrix.
source - Circle or Rectangle or Line object 
target - Circle or Rectangle or Line object
Example:
1
# Initial State
2
p1 = Circle({pos:[0, 0], radius:10, color:rgba(200, 200, 200, .6)})
3
p2 = Circle({pos:[12, 10], radius:10, color:rgba(0, 200, 0, .6)})
4
b1 = Rectangle({pos:[-12, 0], size:[15, 15], color:rgba(200, 0, 0, .6)})
5
mtv1 = Arrow({pos:[p1.pos], color:"green"})
6
mtv2 = Arrow({pos:[p1.pos], color:"red"})
1
# Calculations
2
mtv1.size = getIntersect(p1, p2)
3
mtv2.size = getIntersect(p1, b1)
getIntersectionPoints
This function returns a list containing all the points where the object boundaries intersect. The points are vectors corresponding with the coordinates of those intersection locations. This can be used to identify exactly where the overlap is occurring in your scenarios.
source - Circle or Rectangle or Line  object
target - Circle or Rectangle or Line  object
The image below shows an example of the points of intersection between a rectangle and a line, but note, those points are being showed for demonstration only, and would not be visible unless you assign them to a visible object, in this case the position of two small circle objects.
​
​
Example:
1
# Initial State
2
r = Rectangle({pos:[-4, 0], size:[10,15], color:"orange", opacity:.5})
3
r.rotate(.1)
4
l = Line({pos:[0,10], pos2:[-10, -20]})
1
# Calculations
2
points = getIntersectionPoints(r, ln)
Comparison Functions
The following functions are used to compare two values as being equal or unequal as well as testing if one value is larger or smaller than another. These are very helpful when writing goals for students.
equal(a, b) or a == b
The function tests if two values (x and y) are equal. It returns a boolean value of true or false.
2 + 2 == 3             # returns false
2 + 2 == 4             # returns true
t == 10                # returns true if t is 10, or false if it is not.
equal(2 + 2, 4)        # same as 2 + 2 == 4
deepEqual(a, b)
This function is similar to equal, but it tests element wise whether two matrices are equal. It returns a boolean value of true or false. The code below demonstrates the difference between equal and deepEqual:
p1 = Particle([10, 10])
p2 = Particle([10, 0])
deepEqual(p1.pos, p2.pos)   # returns false
equal(p1.pos, p2.pos)       # returns [true, false]
larger(a, b) or a > b
The function tests if one value (a) is larger than another (b). It returns a boolean value of true or false.
2 > 3               # returns false
3 > 2               # returns true
2 > 2               # returns false
larger(2, 2)        # same as 2 > 2
smaller(a, b) or a < b
The function tests if one value (a) is smaller than another (b). It returns a boolean value of true or false.
2 < 3                # returns true
3 < 2                # returns false
2 < 2                # returns false
smaller(2, 2)        # returns false
unequal(a, b) or a != b
The function tests if two values (a and b) are unequal. It returns a boolean value of true or false.
2 + 2 != 3              # returns true
unequal(2 + 2, 3)       # true -- same as 2 + 2 != 3
2 + 2 != 4              # returns false
t != 10                 # returns false if t is 10, or true if it is not.
Comparison operators return true or false but these also evaluate to 1 (true) or 0 (false). This can allow you to conditionally assign a value to a variable depending on the evaluation of the comparison. See the code below as an example:
# If t is larger than 10, then the value of F is [10, 10], otherwise it is 0.
F = (t > 10) * [10, 10]
if(test, true_result, false_result)
The if() function returns true_result or false_result depending on test.
if(true, 3, 44)                 # returns 3
if(false, 3, 44)                # returns 44
if(1 > 2, 3, 44)                # test is false; therefore returns 44
a = 1
b = 1
if(a == b, "YAY", "darn")       # test is true; therefore returns "YAY"
Logical Operators
The following operators are used to execute logical AND and OR comparisons for the use of evaluating logical statements.
and
This is used for performing a logical AND conjunction. For example, "A and B" is true only if A is true and B is true. "A and B" is false if either A or B is false.
A = true
B = true
A and B         # returns true
B = false
A and B         # returns false
You can use the and operator to test if two comparisons are both true:
x = 2
(x < 3) and (x == 2)  # returns true
(x < 3) and (x != 2)  # returns false
or
This is used for performing a logical OR conjunction. For example, "A or B" is true if A or B is true. "A or B" is false only if A and B are both false.
A = true
B = false
A or B # returns true
A = false
A or B # returns false
You can use the or operator to test if one of two comparisons are true:
x = 2
smaller(x, 3) or equal(x, 3)    # one is true, so returns true
(x < 1) or (x == 3)             # both are false, so returns false
Built-in Classes
Tychos has only a few classes that are used to create the basic simulated objects in the Tychos universe as well as a few tools for analyzing those objects in the simulated world. The graphical  objects in Tychos that can be used are the Cirlcle, the Rectangle, the Arrow, the Line, the Label, and the Spring The tools that can be used for analyzing the behavior of your simulations are the Graph, the Gauge and the Meter. There are also user input objects that can be added to your simulations to make them more interactive: the Toggle, the Slider, the Input, and the Menu controls.
Circle
A Circle  is drawn as a colored circle in the World View. A Circle has a position, a radius, a color, an opacity, a flag for setting its visibility state, and a flag for determining if a motion map should be attached.
Below is the constructor for the Circle class that shows its default values:
Circle(
  {pos:[0,0], 
   radius:10, 
   color:default_color, 
   border_size: 0,
   border_color: default_color,
   border_style: "none"
   image: "",   
   opacity: 1, 
   visible: true, 
   motion_map: false,
   label: {text: "", color: default_color}
  }
) 
pos — The initial position of your Circle in [X,Y] coordinates.
radius — The radius of the circle that is drawn in the World View to represent this particle.
color — The circle will be drawn in this color. Use HTML colors e.g. "#ff3300", "blue".
border_size — The border thickness in pixels.
border_color — The border will be drawn in this color. Use HTML colors e.g. "#ff3300", "blue".
border_style — Sets the border as either solid (default = "none") or "dash" for a dashed border, or "dot" for a dotted border.
image  — A URL that identifies a JPEG, GIF, SVG or PNG image.
opacity — The circle will be drawn with an opacity between 1 and 0, representing 100% opaque to 100% transparent.
visible — The circle can be hidden from view by setting this flag to false. 
motion_map — This flag tells Tychos to attach a series of strobe images called a motion map.
label - You can attach a label to the Circle object by indicating a the text and color of the label. 
These attributes may also be modified on the Circle after it is created. In particular, one will usually change the pos attribute of a Circle in the Calculations editor to show movement. e.g.
# Initial State editor
c = Circle()
c_big = Circle({pos:[50, 0], radius:25})
c_big.color = "red"
c_green = Circle({pos:[100, 0], color: "green", opacity: .5})
# Calculations editor
c.pos = c.pos + [1, 0.25]
Circle.rotate()
Circle objects can be rotated.
Circle.rotate(angle=0, axis=[0, 0]) — Rotates the Circle object by a given angle value in radian units. You can also provide an optional matrix that identifies the axis of rotation. This method should only be called from the Calculations code editor.
Circle.image
Circle objects can also be represented with an image by setting the image attribute of the object. The text must be a URI link to a graphic file that can be a PNG, SVG, GIF, or JPEG image.
rocket = Circle({pos:[0, 0], radius:10})
rocket.image = "https://upload.wikimedia.org/wikipedia/commons/3/3d/Spacecraft.png"
A Circle that looks like a rocket.
The above image also demonstrates the use of the direction function as well as the rotate method:
rocket.rotate(direction(rocket.v))
Circle.label
Circle objects can also be given a text label. This is similar to the Label object.
c.label = {text:"Hello", color:"green"} — This adds a text label to the Circle object that scales to fit inside the circle.
Ellipse
A Ellipse  is drawn as a colored ellipse in the World View. An Ellipse has a position, a size corresponding to its horizontal radius (x) and vertical radius (y) , a color, an opacity, a flag for setting its visibility state, and a flag for determining if a motion map should be attached.
e1 = Ellipse({pos:[0, 0], size:[10,5], color:"green", opacity:.6})
e2 = Ellipse({pos:[10, 0], size:[5,10], color:"blue", opacity:.6})
e3 = Ellipse({pos:[0, -10], size:[5,5], color:"red", opacity:.6})
Three ellipses with different sizes
Below is the constructor for the Ellipse class that shows its default values:
Ellipse(
  {pos:[0,0], 
   size:[10,5], 
   color:default_color, 
   image: "",   
   opacity: 1, 
   visible: true, 
   motion_map: false,
   label: {text: "", color: default_color}
  }
) 
pos — The initial position of your Ellipse in [X,Y] coordinates.
size — Representing the x radius and y radius of the ellipse that is drawn in the World View.
color — The Ellipse will be drawn in this color. Use HTML colors e.g. "#ff3300", "blue".
border_size — The border thickness in pixels.
border_color — The border will be drawn in this color. Use HTML colors e.g. "#ff3300", "blue".
border_style — Sets the border as either solid (default = "none") or "dash" for a dashed border, or "dot" for a dotted border.
image  — A URL that identifies a JPEG, GIF, SVG or PNG image.
opacity — The Ellipse will be drawn with an opacity between 1 and 0, representing 100% opaque to 100% transparent.
visible — The Ellipse can be hidden from view by setting this flag to false. 
motion_map — This flag tells Tychos to attach a series of strobe images called a motion map.
label - You can attach a label to the Ellipse object by indicating a the text and color of the label. 
These attributes may also be modified on the Ellipse after it is created, just like the Circle. 
Ellipse.rotate()
Ellipse objects can be rotated, just like the Circle.
Ellipse.rotate(angle=0, axis=[0, 0]) — Rotates the Ellipse object by a given angle value in radian units. You can also provide an optional matrix that identifies the axis of rotation. This method should only be called from the Calculations code editor.
Ellipse.image
Ellipse objects can also be represented with an image by setting the image attribute of the object. The text must be a URI link to a graphic file that can be a PNG, SVG, GIF, or JPEG image. See the Circle above for more detail.
Ellipse.label
Ellipse objects can also be given a text label. This is similar to the Label object.
e.label = {text:"Hello", color:"green"} — This adds a text label to the Ellipse object that scales to fit inside the ellipse.
Rectangle
A Rectangle is very similar to a Circle but it is represented as a colored rectangle in the World View. A Rectangle has position, width, height, color, opacity, visibility, a motion map flag, as well as a label. Just as with the Circle, Tychos only uses the width and height attributes for display. You can define how these attributes change given the rules of the simulation that you define.
Below is the constructor for the Rectangle class that shows its default values:
Rectangle(
  {pos:[0,0], 
   size:[10,10], 
   color:default_color,
   image: "", 
   opacity: 1, 
   visible: true, 
   motion_map: false,
   label: {text: "", color: default_color}
  }
) 
pos — The initial position of your Rectangle in [X,Y] coordinates.
size — The width and height of the Rectangle that is drawn in the World View to represent this particle.
color — The Rectangle will be drawn in this color. Use HTML colors e.g. "#ff3300", "blue".
border_size — The border thickness in pixels.
border_color — The border will be drawn in this color. Use HTML colors e.g. "#ff3300", "blue".
border_style — Sets the border as either solid (default = "none") or "dash" for a dashed border, or "dot" for a dotted border.
image  — A URL that identifies a JPEG, GIF, SVG or PNG image.
opacity — The Rectangle will be drawn with an opacity between 1 and 0, representing 100% opaque to 100% transparent.
visible — The Rectangle can be hidden from view by setting this flag to false. 
motion_map — This flag tells Tychos to attach a series of strobe images called a motion map.
label - You can attach a label to the Rectangle object by indicating a the text and color of the label. 
These attributes may also be modified on the Rectangle object after it is created. In particular, one will usually change the pos attribute in the Calculations editor to show movement. e.g.
# Initial State editor
r1 = Rectangle({pos:[0, 0], size:[10, 10], color:"green"})
r2 = Rectangle({pos:[20, 0], size:[10, 20], color:"blue"})
r3 = Rectangle({pos:[40, 0], size:[20, 10], color:"orange"})
# Calculations editor
r1.pos = r1.pos + [1, 0.25]
Rectangle.rotate
You can also rotate a Rectangle object in order to simulate rotational behavior.
Rectangle.rotate(angle=0, axis=[0, 0]) — Rotates the Rectangle object by a given angle value in radian units. You can also provide an optional matrix that identifies the center of rotation. This method should only be called from the Calculations code editor.
Three different Rectangle objects rotated at different angles
Example:
# Calculations editor
r1.rotate(-PI/4)
r2.rotate(radians(90))
r3.rotate(radians(45))
Rectangle.image
Just as with Circle objects, Rectangle objects can also be represented with an image by setting the image attribute of the object.
r.image = "https://some.image.url.jpg"
Rectangle.label
Rectangle objects can also be given a text label. This is similar to the Label object.
r.label = {text:"Hello", color:"green"}
This adds a text label to the Rectangle object.
Arrow
The Arrow class represents a graphical arrow and is commonly used to illustrate vectors, but can be used for representing anything in your simulations.
Below is the constructor for the Arrow class that shows its default values:
Arrow(
  {pos:[0,0], 
   size:[1,0], 
   color:default_color,
   components: false,
   stroke: 1, 
   style: "none",
   opacity: 1, 
   visible: true, 
   motion_map: false
  }
)
pos — coordinates for the starting point of the Arrow as an [X,Y] matrix.
size — the vector to illustrate, e.g. [10, 0] will draw an Arrow 10 units to the right.
color — HTML color value for your Arrow, e.g. "red" or "#ff0000".
components — A flag that determines if X and Y components are drawn, a value of true displays the components.
stroke — Stroke value that determines the visual thickness of the Arrow.
style — Sets the arrow line as either solid (default = "none") or "dash" for a dashed arrow, or "dot" for a dotted arrow.
opacity — The Arrow will be drawn with an opacity between 1 and 0, representing 100% opaque to 100% transparent.
visible — The Arrow can be hidden from view by setting this flag to false.
motion_map — This flag tells Tychos to attach a series of strobe images called a motion map.
Arrow without components
Arrow with components
Example — The illustrations above were drawn using these commands:
# Initial State editor
c = Circle({pos:[0,0], color:"green"})
a = Arrow({pos: c.pos, size: [20, 20], color:"purple"})
a.components = true
Line
The Line class draws a line and is commonly used to illustrate some connecting member like a string or cable, but could really represent anything you like.
Below is the constructor for the Line class that shows its default values:
Line(
  {pos:[0,0], 
   pos2:[1,0], 
   color:default_color,
   stroke: 1,
   style: "none", 
   opacity: 1, 
   visible: true, 
   motion_map: false
  }
)
pos — coordinates for the starting point of the Line as an [X,Y] matrix.
pos2 — coordinates of the termination point of the Line as an [X,Y] matrix
color — HTML color value for your Line, e.g. "red" or "#ff0000".
stroke — Stroke value that determines the visual thickness of the Line. This is measured in pixels.
style — Sets the line as either solid (default = "none") or "dash" for a dashed line, or "dot" for a dotted line.
opacity — The Line will be drawn with an opacity between 1 and 0, representing 100% opaque to 100% transparent.
visible — The Line can be hidden from view by setting this flag to false.
motion_map — This flag tells Tychos to attach a series of strobe images called a motion map.
Example:
myLine = Line({pos:[0, 0], pos2: [20, 20], color: "purple", stroke:2})
anotherLine = Line({pos:[0, 0], pos2: [10, 20], color: "green", stroke:10})
PolyLine
The PolyLine class draws a series of connected lines between a given set of points. This object can be used to represent a complex path or a shape other than a circle or rectangle.
Below is the constructor for the PolyLine class that shows its default values:
PolyLine(
  {points:[], 
   color:default_color,
   stroke: 1,
   style: "none" 
   fill: false
   opacity: 1, 
   visible: true, 
   motion_map: false
  }
)
points — an array of points given as [X,Y] matrices.
color — HTML color value for your PolyLine, e.g. "red" or "#ff0000".
stroke — Stroke value that determines the visual thickness of the PolyLine. This is measured in pixels.
style — Can be "none" for solid segments, "dash" for dashed line segments or "dot" for dotted line segments.
fill — Boolean value (true or false) for displaying the PolyLine object as a filled in solid.
opacity — The PolyLine will be drawn with an opacity between 1 and 0, representing 100% opaque to 100% transparent.
visible — The PolyLine can be hidden from view by setting this flag to false.
motion_map — This flag tells Tychos to attach a series of strobe images called a motion map.
PolyLine objects have a number of methods for manipulating the PolyLine points, like adding new points, changing existing points, removing points, etc:
setPoints: (points) -> Set the points for the PolyLine given an array of points. 
translate: (deltaPosition) -> Move all the points according to a matrix [X, Y].
rotate: (angle, axis) -> Transform the points a certain angle measurement about an axis. This axis is relative to the first point in the PolyLine.
npoints(): -> Returns the number of points in the PolyLine.
append: (point) -> Add a point to the end of the PolyLine.
remove: (n) -> Remove a point at the given index. The first point is at index = 0.
unshift: (point) -> Add a point at the beginning of the PolyLine.
shift: () -> Remove the first point in the PolyLine object.
splice: (point, n) -> Add a point into the PolyLine at the specific index position. The first point is at index = 0.
drop: (n) -> Remove all points from the start to the "n" index position from the PolyLine.
dropRight: (n) -> Remove all points from the end of the PolyLine to the "n" index position.
last: () -> Returns the last point in the PolyLine.
first: () -> Returns the first point in the PolyLine.
replace: (point, n) -> Replace the point at "n" index position with a new point.
clear: () -> Remove all the points in the PolyLine.
point: (n) -> Returns the point at that "n" index position.
slice: (start, end) -> Returns the set of points (but does not remove them) from the PolyLine object beginning at the start value and ending at the end index position.
Three PolyLine objects showing different styles and fills.
Example:
star1 = PolyLine({stroke: 3, style:"dash", fill: true, opacity: .2, color: "blue"})
star1.setPoints([[0,75-200], [379-350,161-200],[469-350,161-200],[397-350,215-200], [423-350,301-200], [350-350,250-200], [277-350,301-200], [303-350,215-200], [231-350,161-200], [321-350,161-200], [0,75-200]])
star2 = PolyLine({stroke: 2, style:"none", color: "green"})
star2.setPoints([[0,75-200], [379-350,161-200],[469-350,161-200],[397-350,215-200], [423-350,301-200], [350-350,250-200], [277-350,301-200], [303-350,215-200], [231-350,161-200], [321-350,161-200], [0,75-200]])
star2.translate([100, 100])
star3 = PolyLine({stroke: 3, style:"dot", color: "red"})
star3.setPoints([[0,75-200], [379-350,161-200],[469-350,161-200],[397-350,215-200], [423-350,301-200], [350-350,250-200], [277-350,301-200], [303-350,215-200], [231-350,161-200], [321-350,161-200], [0,75-200]])
star3.translate([-100, 100])
Spring
A Spring is a visual representation of a common elastic connector that displays a given number of coils that dynamically change shape once the dimensions of the  Spring are changed in the Calculations Pane.
Below is the constructor for the Spring class that shows its default values:
Spring(
  {pos:[0,0], 
   pos2:[1,0], 
   color:default_color,
   coils: 5,
   width: 10,
   stroke: 1, 
   opacity: 1, 
   visible: true, 
   motion_map: false
  }
)
pos — coordinates for the starting point of the Spring as an [X,Y] matrix.
pos2 — coordinates of the termination point of the Spring as an [X,Y] matrix
color — HTML color value for your Spring, e.g. "red" or "#ff0000".
coils — The number "coil" zig-zags.
width — The width of the "coil" zig-zags.
stroke — Stroke value that determines the visual thickness of the Spring. This is measured in pixels.
opacity — The Spring will be drawn with an opacity between 1 and 0, representing 100% opaque to 100% transparent.
visible — The Spring can be hidden from view by setting this flag to false.
motion_map — This flag tells Tychos to attach a series of strobe images called a motion map.
Three different Spring objects
The code below shows the three different Spring objects above that have different lengths, widths and coil numbers. The Circle objects are shown just for reference.
# Initial State editor
c1 = Circle({pos:[0, 0], radius:2, color:"green"})
spring1 = Spring({pos:[0, 20], pos2:c1.pos, color:"black", coils:20, width:2})
c2 = Circle({pos:[10, 0], radius:2, color:"green"})
spring2 = Spring({pos:[10, 20], pos2:c2.pos, color:"black", coils:10, width:4})
c3 = Circle({pos:[20, 0], radius:2, color:"green"})
spring3 = Spring({pos:[20, 20], pos2:c3.pos, color:"black", coils:20, width:2})
These attributes may also be modified after the Spring is created.
Label
You can add text labels to any scenario using the Label class.
Below is the constructor for the Label class that shows its default values:
Label(
  {pos:[0,0], 
   size:[10,10], 
   text: "",
   color:default_color, 
   opacity: 1, 
   visible: true, 
   motion_map: false
  }
)
pos — coordinates for the center point of the Label as an [X,Y] matrix.
size — The width and height of the Label as an [X,Y] matrix
text — The text of the Label as a string.
color — HTML color value for your Label, e.g. "red" or "#ff0000".
opacity — The Label will be drawn with an opacity between 1 and 0, representing 100% opaque to 100% transparent.
visible — The Label can be hidden from view by setting this flag to false.
motion_map — This flag tells Tychos to attach a series of strobe images called a motion map.
These attributes may also be modified after the Label object is created. Here is an example of how to make several Label objects:
# Initial State editor
label1 = Label({pos:[0, 100], size:[50, 50], text:"Cat", color:"green"})
label2 = Label({pos:[0, 0], size:[150, 150], text:"Dog", color:"red"})
label3 = Label({pos:[0, -100], size:[50, 50], text:"Mouse", color:"blue"})
Label.rotate
Just as with a Block object or a Particle object, you can rotate a label as shown above:
label3.rotate(PI/4)
Particle (deprecated)
This class has been deprecated. Past scenarios that used this class will still work, but we will no longer maintain this class as part of the Tychos language and we suggest that you switch to the Circle class.
A Particle represents a spherical particle in the simulated world and is drawn as a colored circle in the World View. A particle has position, radius and color.
Particle(pos=[0,0], radius=10, color=default_color) -> returns a Particle
pos — The initial position of your particle in [X,Y] coordinates. If you don't specify a position, the default value of [0,0] is used.
radius — The radius of the circle that is drawn in the World View to represent this particle.
color — The particle will be drawn in this color. Use HTML colors e.g. "#ff3300", "blue".
These attributes may also be modified on the particle after it is created. In particular, one will usually change the pos attribute of a particle in the Calculations editor to show a particle's movement. E.g.
# Initial State editor
p = Particle()
p_big = Particle([50, 0], 25)
p_big.color = "red"
p_green = Particle([100, 0], 10, "green")
​
# Calculations editor
p.pos = p.pos + [1, 0.25]
Particle.rotate()