The Current Divider
Same voltage, current splits in the conductance ratio
I_in = 12mA splits between two parallel branches, R1 = 4kΩ and R2. Moving R2 changes the shares into which the conductances 1/R1 and 1/R2 divide the top bar, and the bottom bar is the current in the R2 branch, the part of the supply current that matches that share. The R2 share on the right of the top bar and the length of the bottom bar are always equal. Raising R2 lowers 1/R2, so that branch current falls too. Set R2 so the R2 branch current reaches the target of 4mA on the orange dashed line.
Parallel branches share the same voltage
Split in parallel, both branches hang between the same two nodes, so the voltage V across them is identical. Written with conductance, Ohm's law gives the branch current as I = V/R = V·G. Here G = 1/R measures how readily current flows. Since V is the same for both branches, the current ratio I2/I1 equals the conductance ratio G2/G1, which is the inverse resistance ratio R1/R2. The branch with less resistance, and so more conductance, takes more current, and that single line, current proportional to conductance, is the whole of current division.
A branch current is the other resistor's share
The total current is the sum of the two branch currents, I_in = V·(G1+G2), so V = I_in/(G1+G2). The R2 branch current is therefore I_2 = V·G2 = I_in·G2/(G1+G2), and the division ratio G2/(G1+G2) is the share of the total conductance that the R2 branch holds. Turning conductance back into resistance, G2/(G1+G2) = (1/R2)/((1/R1)+(1/R2)) = R1/(R1+R2), so the branch current is proportional to the opposite resistor: I_2 = I_in·R1/(R1+R2). Having the opposite R1, not the branch's own R2, in the numerator is the mark of current division; in voltage division the own resistor R2 was the numerator.
The dual mirror of voltage division
Voltage division split voltage by the resistance ratio in series, and current division, its mirror, splits current by the conductance ratio in parallel. A pairing in which series and parallel, voltage and current, and resistance and conductance all swap at once is called a duality, which is why the two formulas have the same shape with only the letters changed. With three or more branches, the conductance form still works as long as the denominator holds the sum of every branch's conductance, but the form with the opposite resistor in the numerator holds only for two branches. With both tools in hand, you can read any node voltage or any branch current in a circuit that mixes series and parallel in a single line.
Back to the first screen
As you raised R2, 1/R2 fell and the current bar for the R2 branch shrank, and it reached the target of 4mA when R2 was 8kΩ (R1 = 4, I_in = 12). The segment the R2 branch held in the top conductance bar and the length of the current bar below matched from start to finish, because both branches had the same voltage and the current split in direct proportion to conductance. In resistances, I_2 = I_in·R1/(R1+R2): the opposite resistor R1 in the numerator is where it flips, mirror-like, from voltage division.