Just because paper notebooks have things called pages doesn't mean a virtual notebooks need to have them. With MagicalPad, you can take notes and brainstorm on a freeform, page-less layout. The app was just updated this week and is currently on sale for 99 cents.
When you first launch the app, you'll see two default notebooks. This is a similar view to what you get with other note-taking apps such as Outline+, Paper, and Penultimate. Unlike these apps, however, MagicalPad's notebooks are filled with limitless workspaces instead of multiple pages.
From the notebooks home screen, you can add or delete notebooks with the two buttons at the bottom. You can rename a notebook but you can't alter the look of the cover of the notebook. There is a settings button in the upper-right corner that lets you turn the alignment guide on and off (we'll get to that in a minute) and choose whether to share a whole workspace or just what's visible on the screen when sharing a PDF or JPEG (we'll double back to sharing options at the end).
To start brainstorming, note taking, outlining, or mind mapping, double tap anywhere on the workspace to add one of two types of element: either a Text Note or a List Note. A text note is a simple box that lets you enter text, while a list note lets you create bulleted or checkbox lists. The default is a bulleted list, but if you tap on the bullet, it turns into a checkbox. (Tap the checkbox to check it off, and tap a checked checkbox to come full circle and return to a bullet.) Tap and hold on either type of note to drag it around on the workspace and reposition it. You can also swipe on an item of a list to indent or "outdent" it, giving you great flexibility with creating and editing outlines as you go. Lastly, if you have the alignment guide setting enabled in settings, you'll see blue lines when dragging a note to assist you in lining it up with the other notes on the workspace.
If you are engaged in a serious brainstorming session, you can use the mind mapping feature to connect and organize your flurry of thoughts. From the mind mapping menu, tap the "Connect selected" button to link two notes. You can also turn on Auto connect to connect new notes to the chain. And using the "Add to right" and "Add below" buttons, you can add new items to your brainstorming tree. I wouldn't say it's connected to mind mapping per se, but smack in the middle of the mind-mapping menu is a toggle switch that lets you choose the default note type that a double tap creates on the workspace.
The formatting button on the toolbar has tabs that let you select background colors for your notes and the workspace itself, along with borders and text formatting. The themes button should display various pleasing color combinations for formatting all the items in a list in an attractive and logical manner, but it didn't work for me. Also helpful is the row at the top of each formatting tab that shows your recent color, border, or text selections.
You can export your MagicalPad creations and import docs to the app. Tap the Share button and you'll see four options: Evernote, Dropbox, Google Drive, and e-mail. I was unable to connect to either of my Google Drive accounts, but I was able to link to my Dropbox account. You can export a MagicalPad workspace as a PDF, a Rich Text doc, an OPML outline, a JPEG, or MagicPad's own format.
MagicalPad is probably a better app for creating lists and outlines and making visual representations of brainstorming sessions than it is for strict note-taking, but it's intuitive no matter your pursuit. For strict note-taking on the iPad, I would steer you toward Notability.