Results of a search for new phenomena in events with at least three photons are reported. Data from proton--proton collisions at a centre-of-mass energy of 8 TeV, corresponding to an integrated luminosity of 20.3 fb$^{-1}$, were collected with the ATLAS detector at the LHC. The observed data are well described by the Standard Model. Limits at the 95% confidence level on new phenomena are presented based on the rate of events in an inclusive signal region and a restricted signal region targeting the rare decay $Z\to 3\gamma$, as well as di-photon and tri-photon resonance searches. For a Standard Model Higgs boson decaying to four photons via a pair of intermediate pseudoscalar particles ($a$), limits are found to be $\sigma \times {\text {BR}}(h \rightarrow aa) \times {\text {BR}}(a \rightarrow \gamma \gamma)^{2} < 10^{-3} \sigma_{\text{SM}}$ for 10 GeV $< m_{a} <$ 62 GeV. Limits are also presented for Higgs boson-like scalars ($H$) for $m_{H} > $ 125 GeV, and for a $Z'$ decaying to three photons via $Z' \rightarrow a+\gamma \rightarrow 3\gamma$. Additionally, the observed limit on the branching ratio of the $Z$ boson decay to three photons is found to be BR$(Z \rightarrow 3\gamma) < 2.2 \times 10^{-6}$, a result five times stronger than the previous result from LEP.