can you calculate the math behind red_cube.x and drop.y?

Here is the exact mathematical breakdown of how red_cube.x and drop.y change across each cycle in your script.

1. drop.y (Raindrop Height)

For each raindrop $i$, let $y_{\text{start}, i}$ be its randomly assigned initial height from random.uniform(0, 4).

• Initial State: $\text{drop}_i.y = y_{\text{start}, i}$
  
  
  
  
• After dash_step_1(): Subtractions of $1$ unit $\rightarrow \text{drop}_i.y = y_{\text{start}, i} - 1$
  
  
  
  
• After dash_step_2(): Subtractions of another $1$ unit $\rightarrow \text{drop}_i.y = y_{\text{start}, i} - 2$
  
  
  
  
• After reset_and_repeat(): Position is reassigned to a brand new random coordinate $y_{\text{new}, i} \in [0, 4]$.
  
  

Total Displacement per sequence run: Each drop moves $-2.0$ units downward on the Y-axis before resetting.

2. red_cube.x (Player Horizontal Position)

The red cube starts at $x_{\text{start}} = -2.0$. Because $x < 0$ initially, the conditionals in your step functions evaluate to true:

$$\text{Initial Position: } x_0 = -2.0 \quad (x_0 < 0) \text{[cite: 3]}$$

During the Sequence:

1. dash_step_1():
   
   
   $$\text{Since } x_0 < 0 \implies x_1 = x_0 - 1 = -2.0 - 1.0 = \mathbf{-3.0} \text{[cite: 3]}$$
2. dash_step_2():
   
   
   $$\text{Since } x_1 < 0 \implies x_2 = x_1 - 1 = -3.0 - 1.0 = \mathbf{-4.0} \text{[cite: 3]}$$

In reset_and_repeat():

Your code evaluates if red_cube.position < 0:. In Ursina, comparing a Vec3 vector to an integer evaluates the vector's length/truthiness or first component, keeping it on the negative branch:

$$x_3 = -\text{start\_pos.x} = -(-2.0) = \mathbf{2.0} \text{[cite: 3]}$$

Subsequent Cycle Behavior:

On the next cycle, because $x$ is now $+2.0$ ($x \ge 0$):

• dash_step_1(): $x = 2.0 + 1 = \mathbf{3.0}$
  
  
  
  
• dash_step_2(): $x = 3.0 + 1 = \mathbf{4.0}$
  
  
  
  
• reset_and_repeat(): Flips back to $\text{start\_pos.x} = \mathbf{-2.0}$
  
  
  
  

Movement Summary Table

Cycle Stage	red_cube.x (Odd Cycles)	red_cube.x (Even Cycles)	drop.y (All Drops)
Start of Cycle	$-2.0$	$+2.0$	$y_{\text{start}}$
After dash_step_1()	$-3.0$	$+3.0$	$y_{\text{start}} - 1.0$
After dash_step_2()	$-4.0$	$+4.0$	$y_{\text{start}} - 2.0$
After reset_and_repeat()	Resets to $+2.0$	Resets to $-2.0$	Resets to new $y \in [0, 4]$

The red cube bounces back and forth across the screen between $[-4.0, +4.0]$ while the raindrops drop $2$ units before getting re-rolled.