I have a two-dimensional uniform data. I have splitted the data on two parts with a threshold.

set.seed(20181116) # set the initial seed for generator
n <- 10000 

data <- data.frame(x=runif(n), y=runif(n))

threshold  <- 0.5      
plot(data, col=ifelse(data$x > threshold/2 & data$x < 3*threshold/2 & data$y < threshold, "red", "black"))

Question. What a statistical tests do I use to show that black and red observations come from a two-dimensional uniform distribution too?

I have a two-dimensional uniform data. I have splitted the data on two parts with a threshold.

set.seed(20181116) # set the initial seed for generator
n <- 10000 

data <- data.frame(x=runif(n), y=runif(n))

threshold  <- 0.5      
plot(data, col=ifelse(data$x > threshold/2 & 
                      data$x < 3*threshold/2 & 
                      data$y < threshold, "red", "black"))

Question. What a statistical tests do I use to show that black and red observations come from a two-dimensional uniform distribution too?