diff --git a/remap_particle_IDs.py b/remap_particle_IDs.py
index 8570272..32efed9 100644
--- a/remap_particle_IDs.py
+++ b/remap_particle_IDs.py
@@ -1,27 +1,48 @@
+from itertools import product
+
 import numpy as np
 
 
-def convert_ID_between_resolutions(particle_ID: int, Nres_from: int, Nres_to: int):
-    particle_k = particle_ID % Nres_from
-    particle_j = ((particle_ID - particle_k) // Nres_from) % Nres_from
-    particle_i = ((particle_ID - particle_k) // Nres_from - particle_j) // Nres_from
-    lowres_ID = ((particle_i * Nres_to) + particle_j) * Nres_to + particle_k
-    return lowres_ID
+def original_position(Nres: int, particle_ID: int):
+    particle_k = particle_ID % Nres
+    particle_j = ((particle_ID - particle_k) // Nres) % Nres
+    particle_i = ((particle_ID - particle_k) // Nres - particle_j) // Nres
+    return np.array([particle_i, particle_j, particle_k])
+
+
+def upscale_IDs(particle_ID: int, Nres_min: int, Nres_max: int):
+    assert Nres_max % Nres_min == 0
+    N = Nres_max // Nres_min
+
+    orig = original_position(Nres_min, particle_ID)
+    mult = orig * N
+    for shift in product(range(N), repeat=3):
+        variant = mult + np.array(shift)
+        yield ((variant[0] * Nres_max) + variant[1]) * Nres_max + variant[2]
+
+
+def downscale_IDs(particle_ID: int, Nres_max: int, Nres_min: int):
+    assert Nres_max % Nres_min == 0
+    N = Nres_max // Nres_min
+
+    orig = original_position(Nres_max, particle_ID)
+    mult = np.floor_divide(orig, N)
+    return ((mult[0] * Nres_min) + mult[1]) * Nres_min + mult[2]
 
 
 if __name__ == "__main__":
-    test_particle = np.array([0, 127, 127])
+    test_particle = np.array([0, 0, 127])
     # maximum_test = np.array([127, 127, 127]) #this works, Nres - 1 is the maximum for (i,j,k)
 
     Nres_1 = 128
     Nres_2 = 256
 
-    particle_ID_1 = ((test_particle[0] * Nres_1) + test_particle[1]) * Nres_1 + test_particle[2]
-    particle_ID_2 = ((test_particle[0] * Nres_2) + test_particle[1]) * Nres_2 + test_particle[2]
+    test_particle_id = ((test_particle[0] * Nres_1) + test_particle[1]) * Nres_1 + test_particle[2]
+    print(test_particle_id)
 
-    print(particle_ID_1, particle_ID_2)
+    particle_ID_1_converted = upscale_IDs(test_particle_id, Nres_1, Nres_2)
 
-    particle_ID_1_converted = convert_ID_between_resolutions(particle_ID_1, Nres_1, Nres_2)
-    particle_ID_1_converted_converted = convert_ID_between_resolutions(particle_ID_1_converted, Nres_2, Nres_1)
-
-    print(particle_ID_1, particle_ID_1_converted, particle_ID_1_converted_converted)
+    for id in particle_ID_1_converted:
+        reverse = downscale_IDs(id, Nres_2, Nres_1)
+        print(id, reverse)
+        assert reverse == test_particle_id