For Affinity Photo elliptical blends, create a layer via the layer menu and then apply a fill via the edit menu and fill, fill it with white, green etc doesn't matter as the color effect will be applied on top of it via live filter layers.
Go to the layer menu and live filter layers and color and procedural texture and apply that to the current layer. Go the + entry on the left and click and then fill in the red channel with rx*rx + ry*ry and also divide the lot by 100,000 or perhaps 10,000 (depends on the document). Also with the rx*rx (relative horizontal so you can move the layer) add a 0.3*rx*rx and for ry part, add a 0.6*ry*ry etc.
You can vary the 0.3 and 0.6 etc by channels and also enter a -0.3 or 2.1 etc instead. Repeat the + button twice to add a green and blue channel and copy the equation into both, and then vary the 0.3 to 0.8 or -0.2 etc so they are all different for each channel.
Go to the blend mode at the bottom of the panel and set to difference. Re-position the origin point for the layer interactively. Close the panel.
You can now select the white box for the entry and right click and select duplicate and that duplicates the live filter layer. You can repeat this five or six times.
You can also double click any of the entries and then modify the origin point for the layer as well as 0.3 and 0.6 etc for the red and green and blue channel.
The combination of the layers and settings will results in a super colorful elliptical design in Affinity Photo and you can merge them all into a pixel layer via the layer menu and merge command
You can add a live procedural texture to a white filled layer (via the layer menu) and for the equation, click the + three times and enter (0.3*rx*rx+0.3*ry*ry)/200000 for the Red and (0.1*rx*rx+0.4*ry*ry)/200000 for the Green and (0.6*rx*rx+0.8*ry*ry)/200000 for the Blue. Set to difference. Close panel. Go to the white box in the layers panel for the live effect and right click and select duplicate and repeat three or four times for a very basic oval color effect without the need to change the origin or change the settings. You can double click any of the entries and change the 0.1 to 0.2 or change it to -1.2 or -3.8 etc or change the 200000 to 100000 etc or change the origin point for the effect. Literally billions of color combos can be create from this single layer.