Why are orbits shown out of plane in popular cartoons of atomic structure? [closed]

Question

The (former) U.S. Atomic Energy Commission had a seal showing a symbolic view of the atom that is unrealistic but instantly recognizable:

Source: https://blog.nuclearsecrecy.com/2012/04/13/friday-image-the-atomic-energy-commission-seal-1949/

This symbol was part of the visual language of the atomic age, used by towns, Disney, General Electric, and unicode (U+269B) starting in 1948 or earlier.

Taking the depicted image literally, this would represent the atom beryllium (because it shows 4 electrons). The blog author in the source points out that the most important part for nuclear energy (the nucleus) might have been shown with more detail. In fact, the current agency uses the word "nuclear" instead of "atomic".

While we know today that electrons behave very differently, I am wondering why the electrons are shown in orbits that are at an angle to each other. Many cartoons of atomic structure do this (the most common one has three orthogonal orbits), and I am sure many pre-date this particular example.

If the inspiration for Bohr's model was the solar system, wouldn't you show the orbits all in the same plane, with different radii like in the solar system, like the image above? Was there something known at the time Bohr formulated the model (or before 1949, when the seal was created) that would motivate out-of-plane orbits (maybe angular momentum) while sticking with the inaccurate Bohr model? Or is this a purely artistic choice, helping to make the cartoon more compelling and three-dimensional?

UPDATE: Bohr's drawing do not look like today's textbook drawings of it. Here is a diagram of Xenon (1921-1923).

Source: https://physicstoday.scitation.org/doi/10.1063/PT.3.1978

The atomic whirl symbol for an atom is often associated with the Rutherford model, even if Rutherford said very little about the position or states of the electrons (perhaps because classical physics did not have a model without contradictions, and a satisfying model required the combination of experimental data with quantum theory). In Rutherford's 1911 book "Radioactive Substances and their Radiations", he states:

So he leaves open whether electrons are spherically distributed or present in concentric paths in a plane, and acknowledges the earlier hypothesis by Nagaoka of a positively charged center with electrons surrounding it in some way (Saturnian or otherwise). At this time, the neutron had not been discovered, and it was not clear where the high-energy electrons of beta radiation came from (from the nucleus or elsewhere).

Answer 1

Similar to coat of arms and traditional principles of vexillology, a good logo balances the provision of enough detail to be recognizable – regardless if it is mounted to a lectern, or on a business card – while avoiding to much detail of information. This is what Tufte describes as aim for a high data-ink ratio

$$ \frac{ \text{data ink} } { \text{total ink} } = \frac{ \text{elements conveying data information} } {\text{all elements of the chart}}$$

with intentional remove of detail within reason (ref). See, for example, the flags of the states, D.C., and territories of the United States of America:

(image source)

– at this scale of representation, many are perceived with some content in their centre. The ones of Texas, New Mexico, Colorado are among those which stand out.

From perspective of chemistry/physics, the depiction of the beryllium atom is an improvement in comparison of the seal of AEC because the finer structure of the atom nucleus. At the same time the model is wrong for that diameter of atomic nuclei are orders of magnitude smaller than atomic diameter – in case of helium $\pu{1 fm}$ (or $\pu{10^{-15} m}$) of the nucleus, and $\pu{1 Å}$ (or $\pu{10^{-10} m}$) for the atom. Hence, a depiction of atom and atom nucleus in a scale in common often was and remains impractical – see e.g. the logo of the IAEA including an off-centered atom nucleus:

(source)

the Polish Nuclear Research Centre:

(source)

or the logo of The Big Bang Theory

(source)