xrandr fails when run from udev

The following excerpt from a Python 3 script "myscript" that is meant to detect the screen layout and refresh it using xrandr works fine when run with sudo /usr/local/bin/myscript or /usr/local/bin/myscript:

xrandr_cmd = Popen("xrandr", shell=True, stdout=PIPE, stderr=STDOUT)

However, when run as a result of the following udev rule:

ACTION="change", SUBSYSTEM="drm", ENV{HOTPLUG}=="1", RUN+="/usr/local/bin/myscript"

it fails, stating that xrandr has returned 1 with the message "Can't open display".

Does anyone know why xrandr would fail when run from a udev rule?

The full script, for those who are curious:

#! /usr/bin/env python3
import os
from subprocess import Popen, PIPE, STDOUT

def log(s):
    home_dir = os.path.expanduser("~")
    #with open (f"{home_dir}/monitor_script.log", "a+") as f:
    with open (f"/home/vedantroy/monitor_script.log", "a+") as f:
        f.write(s)
xrandr = "/usr/bin/xrandr"
xrandr_cmd = Popen(xrandr, shell=True, stdout=PIPE, stderr=STDOUT)
retval = xrandr_cmd.wait()
lines = map(lambda l: l.decode('ascii'), xrandr_cmd.stdout.readlines())
if retval != 0:
    nl = "\n"
    log(f"xrandr returned {retval} with output:\n{nl.join(lines)}")
else:
    layout_cmds = [
        # No monitors plugged in
        f"{xrandr} --auto",
        # Thinkpad T580
        # Monitor plugged into HDMI port
        # Monitor to right of laptop
        f"{xrandr} --output HDMI2 --primary --auto --right-of eDP1"
    ]
    layout = 0
    for line in lines:
        if "HDMI2 connected" in line:
            layout = 1
            break

    layout_cmd_str = layout_cmds[layout]
    layout_cmd = Popen(layout_cmd_str, shell=True)
    retval = layout_cmd.wait()
    if retval != 0:
        log(f"{layout_cmd_str} returnd {retval}")